RESEARCH CENTRE

Inria Paris Centre
at Sorbonne University

IN PARTNERSHIP WITH:

CNRS, Sorbonne Université

2023
ACTIVITY REPORT

Project-Team

CAGE

Control and Geometry

IN COLLABORATION WITH: Laboratoire Jacques-Louis Lions (LJLL)

DOMAIN

Applied Mathematics, Computation and
Simulation

THEME

Optimization and control of dynamic
systems

Contents

Project-Team CAGE

1 Team members, visitors, external collaborators

2 Overall objectives

3 Research program

3.1 Research domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Scientific foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Application domains

4.1 First axis: Quantum control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Second axis: Stability and stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Third axis: Motion planning and optimal control
. . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Fourth axis: Geometric models for vision and sub-Riemannian geometry . . . . . . . . . . .

5 Highlights of the year

5.1 Awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2

3

3
3
4

5
5
6
6
7

7
7

6 New results

7
7
6.1 Quantum control: new results
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
6.2 Stability and stabilization: new results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Motion planning and optimal control: new results . . . . . . . . . . . . . . . . . . . . . . . . 10
6.4 Geometric models for vision and sub-Riemannian geometry: new results . . . . . . . . . . . 13

7 Bilateral contracts and grants with industry

14
7.1 Bilateral contracts with industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
7.2 Bilateral grants with industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

8 Partnerships and cooperations

8.1 International research visitors

15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.1.1 Visits of international scientists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.2 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.2.1 ANR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.2.2 Other national initatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.3 Regional initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9 Dissemination

16
9.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
9.1.1 Scientific events: organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
9.1.2 Journal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
9.1.3 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.1.4 Leadership within the scientific community . . . . . . . . . . . . . . . . . . . . . . . . 18
9.1.5 Scientific expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
9.1.6 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
9.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
9.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
9.2.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
9.2.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

10 Scientific production

20
10.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
10.2 Publications of the year
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.3 Cited publications

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Project-Team CAGE

Creation of the Project-Team: 2018 August 01

Keywords

Computer sciences and digital sciences

A6. – Modeling, simulation and control

A6.1. – Methods in mathematical modeling

A6.1.1. – Continuous Modeling (PDE, ODE)

A6.4. – Automatic control

A6.4.1. – Deterministic control

A6.4.3. – Observability and Controlability

A6.4.4. – Stability and Stabilization

A6.4.5. – Control of distributed parameter systems

A6.4.6. – Optimal control

Other research topics and application domains

B2. – Health

B2.6. – Biological and medical imaging

B4.2.2. – Fusion

B5.2.4. – Aerospace

B5.11. – Quantum systems

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Mario Sigalotti [Team leader, INRIA, Senior Researcher, HDR]

• Ugo Boscain [CNRS, Senior Researcher, HDR]

• Barbara Gris [CNRS, Researcher]

• Kevin Le Balc’H [INRIA, ISFP]

Faculty Members

• Jean-Michel Coron [UNIV PARIS, Emeritus]

• Ihab Haidar [ENSEA, Associate Professor Delegation, from Sep 2023]

• Emmanuel Trélat [Sorbonne Université, Professor, HDR]

Post-Doctoral Fellows

• Wadim Gerner [INRIA, Post-Doctoral Fellow]

• Jeremy Martin [INRIA, Post-Doctoral Fellow]

• Jingrui Niu [INRIA, Post-Doctoral Fellow, from Nov 2023]

• Tommaso Rossi [SORBONNE UNIVERSITE, Post-Doctoral Fellow, from Oct 2023]

• Georgy Scholten [SORBONNE UNIVERSITE, Post-Doctoral Fellow, until Aug 2023]

• Alessandro Socionovo [Sorbonne Université, from Nov 2023]

PhD Students

• Rameaux Agbo Bidi [SORBONNE UNIVERSITE]

• Xiangyu Ma [SORBONNE UNIVERSITE, from Oct 2023]

• Robin Roussel [SORBONNE UNIVERSITE]

• Liang Ruikang [POLYTECH SORBONNE]

• Lucia Tessarolo [SORBONNE UNIVERSITE, from Oct 2023]

Administrative Assistant

• Laurence Bourcier [INRIA]

Visiting Scientists

• Riccardo Adami [ECOLE POLYT. TURIN, until Apr 2023]

• Andrey Agrachev [SISSA, until Mar 2023]

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2 Overall objectives

CAGE’s activities take place in the field of mathematical control theory, with applications in several
directions: control of quantum mechanical systems, stability and stabilization, in particular in presence
of uncertain dynamics, optimal control, and geometric models for vision. Although control theory is
nowadays a mature discipline, it is still the subject of intensive research because of its crucial role in a
vast array of applications. Our focus is on the analytical and geometrical aspects of control applications.
At the core of the scientific activity of the team is the geometric control approach, that is, a distinctive
viewpoint issued in particular from (elementary) differential geometry, to tackle questions of controllabil-
ity, motion planning, stability, and optimal control. The emphasis of such a geometric approach is in
intrinsic properties, and it is particularly well adapted to study nonlinear and nonholonomic phenomena
[77, 53]. The geometric control approach has historically been associated with the development of
finite-dimensional control theory. However, its impact in the study of distributed parameter control
systems and, in particular, systems of controlled partial differential equations has been growing in the
last decades, complementing analytical and numerical approaches by providing dynamical, qualitative,
and intrinsic insight [69]. CAGE has the ambition to be at the core of this development.

One of the features of the geometric control approach is its capability of exploiting symmetries
and intrinsic structures of control systems. Symmetries and intrinsic structures (e.g., Lagrangian or
Hamiltonian structures) can be used to characterize minimizing trajectories, prove regularity properties,
and describe invariants. The geometric theory of quantum control, in particular, exploits the rich
geometric structure encoded in the Schrödinger equation to design adapted control schemes and to
characterize their qualitative properties.

3 Research program

3.1 Research domain

Our contributions are in the area of mathematical control theory, which is to say that we are interested
in the analytical and geometrical aspects of control applications. In this approach, a control system
is modeled by a system of equations (of many possible types: ordinary differential equations, partial
differential equations, stochastic differential equations, difference equations,. . . ), possibly not explicitly
known in all its components, which are studied in order to establish qualitative and quantitative properties
concerning the actuation of the system through the control.

Motion planning is, in this respect, a cornerstone property: it denotes the design and validation of
algorithms for identifying a control law steering the system from a given initial state to (or close to) a
target one. Initial and target positions can be replaced by sets of admissible initial and final states as, for
instance, in the motion planning task towards a desired periodic solution. Many specifications can be
added to the pure motion planning task, such as robustness to external or endogenous disturbances,
obstacle avoidance or penalization criteria. A more abstract notion is that of controllability, which
denotes the property of a system for which any two states can be connected by a trajectory corresponding
to an admissible control law. In mathematical terms, this translates into the surjectivity of the so-called
end-point map, which associates with a control and an initial state the final point of the corresponding
trajectory. The analytical and topological properties of endpoint maps are therefore crucial in analyzing
the properties of control systems.

One of the most important additional objective which can be associated with a motion planning task
is optimal control, which corresponds to the minimization of a cost (or, equivalently, the maximization
of a gain) [105]. Optimal control theory is clearly deeply interconnected with calculus of variations,
even if the non-interchangeable nature of the time-variable results in some important specific features,
such as the occurrence of abnormal extremals [81]. Research in optimal control encompasses different
aspects, from numerical methods to dynamic programming and non-smooth analysis, from regularity of
minimizers to high order optimality conditions and curvature-like invariants.

Another domain of control theory with countless applications is stabilization. The goal in this case
is to make the system converge towards an equilibrium or some more general safety region. The main
difference with respect to motion planning is that here the control law is constructed in feedback form.
One of the most important properties in this context is that of robustness, i.e., the performance of the

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Inria Annual Report 2023

stabilization protocol in presence of disturbances or modeling uncertainties. A powerful framework which
has been developed to take into account uncertainties and exogenous non-autonomous disturbances
is that of hybrid and switched systems [92, 82, 98]. The central tool in the stability analysis of control
systems is that of control Lyapunov function. Other relevant techniques are based on algebraic criteria
or dynamical systems. One of the most important stability property which is studied in the context of
control system is input-to-state stability [96], which measures how sensitive the system is to an external
excitation.

One of the areas where control applications have nowadays the most impressive developments is in
the field of biomedicine and neurosciences. Improvements both in modeling and in the capability of
finely actuating biological systems have concurred in increasing the popularity of these subjects. Notable
advances concern, in particular, identification and control for biochemical networks [90] and models for
neural activity [74]. Therapy analysis from the point of view of optimal control has also attracted a great
attention [94].

Biological models are not the only one in which stochastic processes play an important role. Stock-
markets and energy grids are two major examples where optimal control techniques are applied in the
non-deterministic setting. Sophisticated mathematical tools have been developed since several decades
to allow for such extensions. Many theoretical advances have also been required for dealing with complex
systems whose description is based on distributed parameters representation and partial differential
equations. Functional analysis, in particular, is a crucial tool to tackle the control of such systems [102].
Let us conclude this section by mentioning another challenging application domain for control
theory: the decision by the European Union to fund a flagship devoted to the development of quantum
technologies is a symptom of the role that quantum applications are going to play in tomorrow’s society.
Quantum control is one of the bricks of quantum engineering, and presents many peculiarities with
respect to standard control theory, as a consequence of the specific properties of the systems described
by the laws of quantum physics. Particularly important for technological applications is the capability
of inducing and reproducing coherent state superpositions and entanglement in a fast, reliable, and
efficient way [75].

3.2 Scientific foundations

At the core of the scientific activity of the team is the geometric control approach. One of the features
of the geometric control approach is its capability of exploiting symmetries and intrinsic structures of
control systems. Symmetries and intrinsic structures can be used to characterize minimizing trajectories,
prove regularity properties and describe invariants. An egregious example is given by mechanical systems,
which inherently exhibit Lagrangian/Hamiltonian structures which are naturally expressed using the
language of symplectic geometry [65]. The geometric theory of quantum control, in particular, exploits
the rich geometric structure encoded in the Schrödinger equation to engineer adapted control schemes
and to characterize their qualitative properties. The Lie–Galerkin technique that we proposed starting in
[66] builds on this premises in order to provide powerful tests for the controllability of quantum systems
defined on infinite-dimensional Hilbert spaces.

Although the focus of geometric control theory is on qualitative properties, its impact can also
be disruptive when it is used in combination with quantitative analytical tools, in which case it can
dramatically improve the computational efficiency. This is the case in particular in optimal control.
Classical optimal control techniques (in particular, Pontryagin Maximum Principle, conjugate point
theory, associated numerical methods) can be significantly improved by combining them with powerful
modern techniques of geometric optimal control, of the theory of numerical continuation, or of dynamical
system theory [101, 93]. Geometric optimal control allows the development of general techniques,
applying to wide classes of nonlinear optimal control problems, that can be used to characterize the
behavior of optimal trajectories and in particular to establish regularity properties for them and for the
cost function. Hence, geometric optimal control can be used to obtain powerful optimal syntheses results
and to provide deep geometric insights into many applied problems. Numerical optimal control methods
with geometric insight are in particular important to handle subtle situations such as rigid optimal paths
and, more generally, optimal syntheses exhibiting abnormal minimizers.

Optimal control is not the only area where the geometric approach has a great impact. Let us mention,
for instance, motion planning, where different geometric approaches have been developed: those based

Project CAGE

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on the Lie algebra associated with the control system [86, 83], those based on the differentiation of
nonlinear flows such as the return method [70, 71], and those exploiting the differential flatness of the
system [73].

Geometric control theory is not only a powerful framework to investigate control systems, but also a
useful tool to model and study phenomena that are not a priori control-related. Two occurrences of this
property play an important role in the activities of CAGE:

• geometric control theory as a tool to investigate properties of mathematical structures;

• geometric control theory as a modeling tool for neurophysical phenomena and for synthesizing

biomimetic algorithms based on such models.

Examples of the first type, concern, for instance, hypoelliptic heat kernels [52] or shape optimization
[56]. Examples of the second type are inactivation principles in human motricity [58] or neurogeometrical
models for image representation of the primary visual cortex in mammals [63].

A particularly relevant class of control systems, both from the point of view of theory and applications,
is characterized by the linearity of the controlled vector field with respect to the control parameters. When
the controls are unconstrained in norm, this means that the admissible velocities form a distribution in
the tangent bundle to the state manifold. If the distribution is equipped with a point-dependent quadratic
form (encoding the cost of the control), the resulting geometrical structure is said to be sub-Riemannian.
Sub-Riemannian geometry appears as the underlying geometry of nonlinear control systems: in a similar
way as the linearization of a control system provides local informations which are readable using the
Euclidean metric scale, sub-Riemannian geometry provides an adapted non-isotropic class of lenses
which are often much more informative. As such, its study is fundamental for control design. The
importance of sub-Riemannian geometry goes beyond control theory and it is an active field of research
both in differential geometry [85], geometric measure theory [54] and hypoelliptic operator theory [59].

4 Application domains

4.1 First axis: Quantum control

Quantum control is one of the bricks of quantum engineering, since manipulation of quantum mechan-
ical systems is ubiquitous in applications such as quantum computation, quantum cryptography, and
quantum sensing (in particular, imaging by nuclear magnetic resonance).

Quantum control presents many peculiarities with respect to standard control theory, as a con-
sequence of the specific properties of the systems described by the laws of quantum physics. Particularly
important for technological applications is the capability of inducing and reproducing coherent state
superpositions and entanglement in a fast, reliable, and efficient way. The efficiency of the control action
has a dramatic impact on the quality of the coherence and the robustness of the required manipulation.
Minimal time constraints and interaction of time scales are important factors for characterizing the effi-
ciency of a quantum control strategy. CAGE works for the improvement of quantum control paradigms,
especially for what concerns quantum systems evolving in infinite-dimensional Hilbert spaces. The
controllability of quantum system is a well-established topic when the state space is finite-dimensional
[72], thanks to general controllability methods for left-invariant control systems on compact Lie groups
[64, 78]. When the state space is infinite-dimensional, it is known that in general the bilinear Schrödinger
equation is not exactly controllable [103]. The Lie–Galerkin technique [66] combines finite-dimensional
geometric control techniques and the distributed parameter framework in order to provide the most
powerful available tests for the approximate controllability of quantum systems defined on infinite-
dimensional Hilbert spaces. Another important technique to the development of which we contribute is
adiabatic quantum control. Adiabatic approximation theory and, in particular, adiabatic evolution [87,
99, 106] is well-known to improve the robustness of the control strategy and is strongly related to time
scales analysis. The advantage of the adiabatic control is that it is constructive and produces control laws
which are both smooth and robust to parameter uncertainty [107, 80, 62].

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Inria Annual Report 2023

4.2 Second axis: Stability and stabilization

A control application with a long history and still very challenging open problems is stabilization. For
infinite-dimensional systems, in particular nonlinear ones, the richness of the possible functional analyt-
ical frameworks makes feedback stabilization a challenging and active domain of research. Of particular
interest are the different types of stabilization that may be obtained: exponential, polynomial, finite-time,
. . . Another important aspect of stabilization concerns control of systems with uncertain dynamics, i.e.,
with dynamics including possibly non-autonomous parameters whose value and dependence on time
cannot be anticipated. Robustification, i.e., offsetting uncertainties by suitably designing the control
strategy, is a widespread task in automatic control theory, showing up in many applicative domains such
as electric circuits or aerospace motion planning. If dynamics are not only subject to static uncertainty,
but may also change as time goes, the problem of controlling the system can be recast within the the-
ory of switched and hybrid systems, both in a deterministic and in a probabilistic setting. Switched
and hybrid systems constitute a broad framework for the description of the heterogeneous systems in
which continuous dynamics (typically pertaining to physical quantities) interact with discrete/logical
components. The development of the switched and hybrid paradigm has been motivated by a broad
range of applications, including automotive and transportation industry [95], energy management [88]
and congestion control [84]. Even if both controllability [97] and observability [79] of switched and
hybrid systems raise several important research issues, the central role in their study is played by uniform
stability and stabilizabilization [82, 98]. Uniformity is considered with respect to all signals in a given
class, and it is well-known that stability of switched systems depends not only on the dynamics of each
subsystem but also on the properties of the considered class of switching signals. In many situations
it is interesting for modeling purposes to specify the features of the switched system by introducing
constrained switching rules. A typical constraint is that each mode is activated for at least a fixed
minimal amount of time, called the dwell-time. Our approach to constrained switching is based on the
idea of relating the analytical properties of the classes of constrained switching laws (shift-invariance,
compactness, closure under concatenation, . . . ) to the stability behavior of the corresponding switched
systems. One can introduce probabilistic uncertainties by endowing the classes of admissible signals
with suitable probability measures. The interest of this approach is that probabilistic stability analysis
filters out highly ‘exceptional’ worst-case trajectories. Although less explicitly characterized from a dy-
namical viewpoint than its deterministic counterpart, the probabilistic notion of uniform exponential
stability can be studied using several reformulations of Lyapunov exponents proposed in the literature
[57, 68, 104].

4.3 Third axis: Motion planning and optimal control

Geometric optimal control allows the development of general techniques, applying to wide classes of
nonlinear optimal control problems, that can be used to characterize the behavior of optimal trajectories
and in particular to establish regularity properties for them and for the cost function. Hence, geometric
optimal control can be used to obtain powerful optimal syntheses results and to provide deep geometric
insights into many applied problems. Geometric optimal control methods are in particular important to
handle subtle situations such as rigid optimal paths and, more generally, optimal syntheses exhibiting
abnormal minimizers.

Although the focus of geometric control theory is on qualitative properties, its impact can also
be disruptive when it is used in combination with quantitative analytical tools, in which case it can
dramatically improve the computational efficiency. This is the case in particular in optimal control.
Classical optimal control techniques (in particular, Pontryagin Maximum Principle, conjugate point
theory, associated numerical methods) can be significantly improved by combining them with powerful
modern techniques of geometric optimal control, of the theory of numerical continuation, or of dynamical
system theory [101, 93]. Applications of optimal control theory considered by CAGE concern, in particular,
motion planning problems for aerospace (atmospheric re-entry, orbit transfer, low cost interplanetary
space missions, . . . ) [60, 100].

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4.4 Fourth axis: Geometric models for vision and sub-Riemannian geometry

Geometric control theory is not only a powerful framework to investigate control systems, but also a useful
tool to model and study phenomena that are not a priori control-related. In particular, we use control
theory to investigate the properties of sub-Riemannian structures, both for the sake of mathematical
understanding and as a modeling tool for image and sound perception and processing . We recall that sub-
Riemannian geometry is a geometric framework which is used to measure distances in nonholonomic
contexts and which has a natural and powerful optimal control interpretation in terms control-linear
systems with quadratic cost. Sub-Riemannian geometry, and in particular the theory of their associated
(hypoelliptic) diffusive processes, plays a crucial role in the neurogeometrical model of the primary visual
cortex due to Petitot, Citti and Sarti, based on the functional architecture first described by Hubel and
Wiesel [76, 89, 67, 91]. Such a model can be used as a powerful paradigm for bio-inspired image processing,
as already illustrated in the literature [63, 61]. Our contributions to geometry of vision are based not only
on this approach, but also on another geometric and sub-Riemannian framework for vision, based on
pattern matching in the group of diffeomorphisms. In this case admissible diffeomorphisms correspond
to deformations which are generated by vector fields satisfying a set of nonholonomic constraints. A
sub-Riemannian metric on the infinite-dimensional group of diffeomorphisms is induced by a length on
the tangent distribution of admissible velocities [55]. Nonholonomic constraints can be especially useful
to describe distortions of sets of interconnected objects (e.g., motions of organs in medical imaging).

5 Highlights of the year

5.1 Awards

Rémi Robin was awarded with the Prix solennel de thèse de la chancellerie de Paris, the Prix de thèse
PGMO 2023, and the Prix de thèse SMAI-GAMNI for his PhD thesis defended in 2022 and obtained while
being member of the team CAGE.

Daniele Cannarsa and Mario Sigalotti have been awarded the Brockett-Willems Outstanding Paper
Award 2023 for the best paper published in Systems & Control Letters during the two-year period from
January 2021 through December 2022 (paper written while Daniele Cannarsa was member of the team
CAGE).

6 New results

6.1 Quantum control: new results

Let us list here our new results in quantum control theory.

• Achiral molecules can be made temporarily chiral by excitation with electric fields, in the sense
that an average over molecular orientations displays a net chiral signal. In [46], we go beyond
the assumption of molecular orientations to remain fixed during the excitation process. Treating
both rotations and vibrations quantum mechanically, we identify conditions for the creation of
chiral vibrational wavepackets – with net chiral signals – in ensembles of achiral molecules which
are initially randomly oriented. Based on the analysis of symmetry and controllability, we derive
excitation schemes for the creation of chiral wavepackets using a combination of (a) microwave
and IR pulses and (b) a static field and a sequence of IR pulses. These protocols leverage quantum
rotational dynamics for pump-probe spectroscopy of chiral vibrational dynamics, extending the
latter to regions of the electromagnetic spectrum other than the UV.

• In [48], we explore the controllability of a closed multi-input control-affine quantum system.
Previous studies have demonstrated that a spectrum connected by conical intersections which
do not pile up yields exact controllability in finite dimension and approximate controllability in
infinite dimension. Actually, the property that intersections between eigenvalues are conical and
that they do not pile up is generic. However, in physical situations, due to symmetry of the system,
the spectrum can exhibit intersections that are not conical and possibly pile up. We extend the

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Inria Annual Report 2023

controllability result to cover this type of situations under the hypothesis that the intersections
have at least one conical direction and the piled-up intersections have "rationally unrelated germs".
Finally, we provide a testable first-order sufficient condition for controllability. Physically relevant
examples are provided.

• In [45], we obtain observability estimates for Schrödinger equations in the plane. More precisely,
considering a periodic bounded potential, we prove that the evolution Schrödinger equation
is observable from any periodic measurable set, in any small time. We then extend Taüffer’s
recent result in the two-dimensional case to less regular observable sets and general bounded
periodic potentials. The methodology of the proof is based on the use of the Floquet-Bloch
transform, Strichartz estimates and semiclassical defect measures for the obtention of observability
inequalities for a family of Schrödinger equations posed on the torus.

• In [20], we study, in the semiclassical sense, the global approximate controllability in small time
of the quantum density and quantum momentum of the 1-D semiclassical cubic Schrödinger
equation with two controls between two states with positive quantum densities. We first con-
trol the asymptotic expansions of the zeroth and first order of the physical observables via the
Agrachev–Sarychev method. Then we conclude the proof through techniques of semiclassical
approximation of the nonlinear Schrödinger equation.

• In [26], we establish some properties of quantum limits on a product manifold, proving for instance
that, under appropriate assumptions, the quantum limits on the product of manifolds are absolutely
continuous if the quantum limits on each manifolds are absolutely continuous. On a product
of Riemannian manifolds satisfying the minimal multiplicity property, we prove that a periodic
geodesic can never be charged by a quantum limit.

6.2 Stability and stabilization: new results

Let us list here our new results about stability and stabilization of control and hybrid systems.

• In [23], we study some spectral properties of the scalar dynamical system defined by a linear delay-
differential equation with two positive delays. More precisely, the existing links between the delays
and the maximal multiplicity of the characteristic roots are explored, as well as the dominancy
of such roots compared with the spectrum localization. As a by-product of the analysis, the pole
placement issue is revisited with more emphasis on the role of the delays as control parameters in
defining a partial pole placement guaranteeing the closed-loop stability with an appropriate decay
rate of the corresponding dynamical system.

• In [18], we consider the problem of determining the stability properties, and in particular assessing
the exponential stability, of a singularly perturbed linear switching system. One of the challenges of
this problem arises from the intricate interplay between the small parameter of singular perturba-
tion and the rate of switching as both tend to zero. Our approach consists in characterizing suitable
auxiliary linear systems that provide lower and upper bounds for the asymptotics of the maximal
Lyapunov exponent of the linear switching system as the parameter of the singular perturbation
tends to zero.

• In [29], we discuss the notion of universality for classes of candidate common Lyapunov functions of
linear switched systems. On the one hand, we prove that a family of absolutely homogeneous func-
tions is universal as soon as it approximates arbitrarily well every convex absolutely homogeneous
function for the C0 topology of the unit sphere. On the other hand, we prove several obstructions
for a class to be universal, showing, in particular, that families of piecewise-polynomial continuous
functions whose construction involves at most l polynomials of degree at most m (for given positive
integers l,m) cannot be universal.

• One of the central questions in control theory is achieving stability through feedback control.
The paper [31] introduces a novel approach that combines Reinforcement Learning (RL) with
mathematical analysis to address this challenge, with a specific focus on the Sterile Insect Technique

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(SIT) system. The objective is to find a feedback control that stabilizes the mosquito population
model. Despite the mathematical complexities and the absence of known solutions for this specific
problem, our RL approach identifies a candidate solution for an explicit stabilizing control. This
study underscores the synergy between AI and mathematics, opening new avenues for tackling
intricate mathematical problems.

• Consider a non-autonomous continuous-time linear system in which the time-dependent matrix
determining the dynamics is piecewise constant and takes finitely many values A1, . . . , AN . The
paper [19] studies the equality cases between the maximal Lyapunov exponent associated with
the set of matrices {A1, . . . , AN }, on the one hand, and the corresponding ones for piecewise de-
terministic Markov processes with modes A1, . . . , AN , on the other hand. A fundamental step in this
study consists in establishing a result of independent interest, namely, that any sequence of Markov
processes associated with the matrices A1, . . . , AN converges, up to extracting a subsequence, to a
Markov process associated with a suitable convex combination of those matrices.

• The article [39] deals with the stability of linear periodic difference delay systems, where the value
at time t of a solution is a linear combination with periodic coefficients of its values at finitely many
delayed instants t − τ1, . . . , t − τN . We establish a necessary and sufficient condition for exponential
stability of such systems when the coefficients have Hölder-continuous derivative, that generalizes
the one obtained for difference delay systems with constant coefficients by Henry and Hale in the
1970s. This condition may be construed as analyticity, in a half plane, of the (operator valued)
harmonic transfer function of an associated linear control system.

• In [35], we explicitly compute the maximal Lyapunov exponent for a switched system on SL2(R).
This computation is reduced to the characterization of optimal trajectories for an optimal control
problem on the Lie group.

• In [38], we prove the (uniform) global exponential stabilization of the cubic defocusing Schrödinger
equation on the torus d-dimensional torus, for d=1, 2 or 3, with a linear damping localized in a
subset of the torus satisfying some geometrical assumptions. In particular, this answers an open
question of Dehman, Gérard, Lebeau from 2006. Our approach is based on three ingredients. First,
we prove the well-posedness of the closed-loop system in Bourgain spaces. Secondly, we derive
new Carleman estimates for the nonlinear equation by directly including the cubic term in the
conjugated operator. Thirdly, by conjugating with energy estimates and Morawetz multipliers
method, we then deduce quantitative observability estimates leading to the uniform exponential
decay of the total energy of the system. As a corollary of the global stabilization result, we obtain an
upper bound of the minimal time of the global null-controllability of the nonlinear equation by
using a stabilization procedure and a local null-controllability result.

• The Sterile Insect Technique or SIT is presently one of the most ecological methods for controlling
insect pests responsible for disease transmission or crop destruction worldwide. This technique
consists of releasing sterile males into the insect pest population. This approach aims at reducing
fertility in the population and, consequently, reduce significantly the native insect population after a
few generations. In the work [32], we study the global stabilization of a pest population at extinction
equilibrium by the SIT method. We construct explicit feedback laws that stabilize the model and
do numerical simulations to show the efficiency of our feedback laws. The different feedback laws
are also compared taking into account their possible implementation in field interventions.

• In the article [24], we study the problem of stabilizing the traffic flow on a ring road to a uniform
steady-state using autonomous vehicles (AV). Traffic is represented at a microscopic level via a
Bando-Follow-the-Leader model capable of reproducing phantom jams. For the single-lane case, a
single AV can stabilize an arbitrary large ring road with an arbitrary large number of cars. Moreover,
this stabilization is exponentially quick with a decay rate independent of the number of cars and a
control gain also independent of the number of cars. On the other side, the stabilization domain and
stabilization time depend on the number of cars. Two types of controller algorithms are proposed:
a proportional control and a proportional-integral control. In both cases, the measurements used
by the controller only depend on the local data around the AV, enabling an easy implementation.

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After numerical tests of the single-lane case, a multilane model is described using a safety-incentive
mechanism for lane change. Numerical simulations for the multilane ring road suggest that the
control strategy is also very efficient in such a setting, even with a single AV.

6.3 Motion planning and optimal control: new results

Let us list here our new results on controllability and motion planning algorithms, including optimal
control, optimization beyond the quantum control framework.

• In [27], we address the problem of catching all speed 1 geodesics of a Riemannian manifold
with a moving ball: given a compact Riemannian manifold (M , g ) and small parameters ϵ > 0
and v > 0, is it possible to find T > 0 and an absolutely continuous map x : [0, T ] → M ,t (cid:55)→ x(t )
satisfying ∥ ˙x∥∞ ≤ v and such that any geodesic of (M , g ) traveled at speed 1 meets the open ball
Bg (x(t ), ϵ) ⊂ M within time T ? Our main motivation comes from the control of the wave equation:
our results show that the controllability of the wave equation can sometimes be improved by
allowing the domain of control to move adequately, even very slowly. We first prove that, in any
Riemannian manifold (M , g ) satisfying a geodesic recurrence condition (GRC), our problem has a
positive answer for any ϵ > 0 and v > 0, and we give examples of Riemannian manifolds (M , g ) for
which (GRC) is satisfied.

• In the lecture notes [51] we introduce controllability, tabilization and optimal control for systems

in finite and infinite dimension.

• In [25], we prove the small-time global null-controllability of forward (resp. backward) semilinear
stochastic parabolic equations with globally Lipschitz nonlinearities in the drift and diffusion terms
(resp. in the drift term). In particular, we solve the open question posed by S. Tang and X. Zhang, in
2009. We propose a new twist on a classical strategy for controlling linear stochastic systems. By
employing a new refined Carleman estimate, we obtain a controllability result in a weighted space
for a linear system with source terms. The main novelty here is that the Carleman parameters are
made explicit and are then used in a Banach fixed point method. This allows to circumvent the
well-known problem of the lack of compactness embeddings for the solutions spaces arising in the
study of controllability problems for stochastic PDEs.

• The article [42] deals with the controllability of linear one-dimensional hyperbolic systems. Re-
formulating the problem in terms of linear difference equations and making use of infinite-
dimensional realization theory, we obtain both necessary and sufficient conditions for approximate
and exact controllability, expressed in the frequency domain. The results are applied to flows in
networks.

• In [36], we consider a linear quadratic (LQ) optimal control problem in both finite and infinite
dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon
T tends to infinity. The leading term in this expansion, proportional to T , corresponds to the
optimal value attained through the classical turnpike theory in the associated static problem. The
remaining terms are associated with optimal stabilization problems towards the turnpike.

• In [16], we deal with the global exact controllability to the trajectories of the Boussinesq system
posed in 2D or 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier slip-
with-friction boundary condition and a Robin boundary condition is im- posed to the temperature.
We assume that one can act on the velocity and the temperature on a small part of the boundary.
For the proof, we first transform the boundary control problem into a distributed control problem.
Then, we prove a global approximate controllability result by adapting the strategy of Coron et al [J.
Eur. Math. Soc., 22 (2020), pp. 1625–1673]; this relies on the controllability properties of the inviscid
Boussinesq system and the analysis of appropriate asymptotic boundary layer expansions. Finally,
we conclude with a local control- lability result; as in many other cases, this can be established as
a consequence of the null controllability of a linearized system through a fixed-point argument.
Our contribution can be viewed as an extension of the results in [J. Eur. Math. Soc., 22 (2020), pp.
1625–1673], where thermal effects were not considered. Thus, we prove that the ideas behind the

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controllability properties of the Euler system and the well-prepared dissipation technique can be
adapted to the present situation. Furthermore, we cover all the classical boundary conditions for
the temperature, that is, those of the Robin, Neumann and Dirichlet kinds.

• The article [17] deals with the controllability of finite-dimensional linear difference delay equations,
i.e., dynamics for which the state at a given time t is obtained as a linear combination of the
control evaluated at time t and of the state evaluated at finitely many previous instants of time
t − Λ1, . . . , t − ΛN . Based on the realization theory developed by Y.Yamamoto for general infinite-
dimensional dynamical systems, we obtain necessary and sufficient conditions, expressed in the
frequency domain, for the approximate controllability in finite time in Lq spaces, q ∈ [1, +∞). We
also provide a necessary condition for L1 exact controllability, which can be seen as the closure of
the L1 approximate controllability criterion. Furthermore, we provide an explicit upper bound on
the minimal times of approximate and exact controllability, given by d max{Λ1, . . . , ΛN }, where d is
the dimension of the state space.

• In [50], we consider the internal control of linear parabolic equations through on-off shape controls,
i.e., controls of the form M (t )χω(t ) with M (t ) ≥ 0 and ω(t ) with a prescribed maximal measure.
We establish small-time approximate controllability towards all possible final states allowed by
the comparison principle with nonnegative controls. We manage to build controls with constant
amplitude M (t ) ≡ ¯M . In contrast, if the moving control set ω(t ) is confined to evolve in some region
of the whole domain, we prove that approximate controllability fails to hold for small times. The
method of proof is constructive. Using Fenchel-Rockafellar duality and the bathtub principle, the
on-off shape control is obtained as the bang-bang solution of an optimal control problem, which
we design by relaxing the constraints. Our optimal control approach is outlined in a rather general
form for linear constrained control problems, paving the way for generalisations and applications
to other PDEs and constraints.

• The goal of [21] is to obtain observability estimates for non-homogeneous elliptic equations in
the presence of a potential, posed on a smooth bounded domain Ω in 2d and observed from a
non-empty open subset ω ⊂ Ω. More precisely, for every real-valued bounded potential V , our
main result shows that, when Ω has a finite number of holes, the observability constant of the
0 (Ω), is of the form C exp(C |V |1/2 log1/2(|V |)) where
elliptic operator −∆ + V , with domain H 2 ∩ H 1
C is a positive constant depending only on Ω and ω. Our methodology of proof is crucially based
on the one recently developed by Logunov, Malinnikova, Nadirashvili, and Nazarov, in the context
of the Landis conjecture on exponential decay of solutions to homogeneous elliptic equations
in the plane. The main difference and additional difficulty is that the zero set of the solutions to
elliptic equations with source term can be very intricate and should be dealt with carefully. As a
consequence of these new observability estimates, we obtain new results concerning control of
semi-linear elliptic equations in the spirit of Fernández-Cara, Zuazua’s open problem concerning
small-time global null-controllability of slightly super-linear heat equations.

′ = f0(q) + (cid:80)k

• In [33], we consider a smooth system of the form q

i =1 ui fi (q), q ∈ M , ui ∈ R, and study
controllability issues on the group of diffeomorphisms of M . It is well-known that the system can ar-
bitrarily well approximate the movement in the direction of any Lie bracket polynomial of f1, . . . , fk .
Any Lie bracket polynomial of f1, . . . , fk is good in this sense. Moreover, some combinations of Lie
brackets which involve the drift term f0 are also good but surely not all of them. In this paper we
try to characterize good ones and, in particular, all universal good combinations, which are good
for any nilpotent truncation of any system.

• In [12], we consider a mechanical system of three ants on the floor, which move according to two
independt rules: Rule A - forces the velocity of any given ant to always point at a neighboring ant,
and Rule B - forces the velocity of every ant to be parallel to the line defined by the two other ants.
We observe that Rule A equips the 6-dimensional configuration space of the ants with a structure of
a homogeneous (3,6) distribution, and that Rule B foliates this 6-dimensional configuration space
onto 5-dimensional leaves, each of which is equiped with a homogeneous (2,3,5) distribution. The
symmetry properties and Bryant-Cartan local invariants of these distributions are determined.
In the case of Rule B we study and determine the singular trajectories (abnormal extremals) of

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the corresponding distributions. We show that these satisfy an interesting system of two ODEs of
Fuchsian type.

• In the work [43], we present a general framework which guarantees the existence of optimal
domains for isoperimetric problems within the class of C 1,1-regular domains satisfying a uniform
ball condition as long as the desired objective function satisfies certain properties. We then verify
that the helicity isoperimetric problem studied by Cantarella, DeTurck, Gluck and Teytel in 2002
satisfies the conditions of our framework and hence establish the existence of optimal domains
within the given class of domains. We additionally use the same framework to prove the existence
of optimal domains among uniform C 1,1-domains for a first curl eigenvalue problem which has
been studied recently for other classes of domains.

• In [44], we investigate properties of the image and kernel of the Biot-Savart operator in the context
of stellarator designs for plasma fusion. We first show that for any given coil winding surface (CWS)
the image of the Biot-Savart operator is L2-dense in the space of square-integrable harmonic fields
defined on a plasma domain surrounded by the CWS. Then we show that harmonic fields which are
harmonic in a proper neighbourhood of the underlying plasma domain can in fact be approximated
in any C k -norm by elements of the image of the Biot-Savart operator. In the second part of this
work we establish an explicit isomorphism between the space of harmonic Neumann fields and the
kernel of the Biot-Savart operator which in particular implies that the dimension of the kernel of
the Biot-Savart operator coincides with the genus of the coil winding surface and hence turns out to
be a homotopy invariant among regular domains in 3-space. Lastly, we provide an iterative scheme
2 ,2-topology to elements of the kernel of the Biot-Savart
which we show converges weakly in W
operator.

− 1

• In [37], considering a general nonlinear dissipative finite dimensional optimal control problem
in fixed time horizon T , we establish a two-term asymptotic expansion of the value function as
T → +∞. The dominating term is T times the optimal value obtained from the optimal static
problem within the classical turnpike theory. The second term, of order unity, is interpreted as the
sum of two values associated with optimal stabilization problems related to the turnpike.

• The turnpike phenomenon stipulates that the solution of an optimal control problem in large time,
remains essentially close to a steady-state of the dynamics, itself being the optimal solution of an
associated static optimal control problem. Under general assumptions, it is known that not only
the optimal state and the optimal control, but also the adjoint state coming from the application
of the Pontryagin maximum principle, are exponentially close to a steady-state, except at the
beginning and at the end of the time frame. In such results, the turnpike set is a singleton, which
is a steady-state. In the paper [30], we establish a turnpike result for finite-dimensional optimal
control problems in which some of the coordinates evolve in a monotone way, and some others are
partial steady-states of the dynamics. We prove that the discrepancy between the optimal trajectory
and the turnpike set is then linear, but not exponential: we thus speak of a linear turnpike theorem.

• Consider, on the one part, a general nonlinear finite-dimensional optimal control problem and
assume that it has a unique solution whose state is denoted by x
. On the other part, consider
the sampled-data control version of it. Under appropriate assumptions, in [41], we prove that
the optimal state of the sampled-data problem converges uniformly to x
as the norm of the
corresponding partition tends to zero. Moreover, applying the Pontryagin maximum principle to
both problems, we prove that, if x
has a unique weak extremal lift with a costate p that is normal,
then the costate of the sampled-data problem converges uniformly to p. In other words, under a
nondegeneracy assumption, control sampling commutes, at the limit of small partitions, with the
application of the Pontryagin maximum principle.

∗

∗

∗

• In this paper [34], we prove Morse index theorems for a big class of constrained variational problems
on graphs. Such theorems are useful in various physical and geometric applications. Our formulas
compute the difference of Morse indices of two Hessians related to two different graphs or two
different sets of boundary conditions. Several applications such as the iteration formulas or lower
bounds for the index are proved.

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• The work [49] tackles the open pit planning problem in an optimal control framework. We study
the optimality conditions for the so-called continuous formulation using Pontryagin’s Maximum
Principle, and introduce a new, semi-continuous formulation that can handle the optimization of a
two-dimensional mine profile. Numerical simulations are provided for several test cases, including
global optimization for the one-dimensional final open pit, and first results for the two-dimensional
sequential open pit. Theses indicate a good consistency between the different approaches, and
with the theoretical optimality conditions.

• In the paper [14], we consider a measure-theoretical formulation of the training of NeurODEs in
the form of a mean-field optimal control with L2-regularization of the control. We derive first order
optimality conditions for the NeurODE training problem in the form of a mean-field maximum
principle, and show that it admits a unique control solution, which is Lipschitz continuous in time.
As a consequence of this uniqueness property, the mean-field maximum principle also provides a
strong quantitative generalization error for finite sample approximations. Our derivation of the
mean-field maximum principle is much simpler than the ones currently available in the literature
for mean-field optimal control problems, and is based on a generalized Lagrange multiplier theorem
on convex sets of spaces of measures. The latter is also new, and can be considered as a result of
independent interest.

6.4 Geometric models for vision and sub-Riemannian geometry: new results

Let us list here our new results in the geometry of vision axis and, more generally, on hypoelliptic diffusion
and sub-Riemannian geometry.

• In the article [28], we study the observability (or, equivalently, the controllability) of some subelliptic
evolution equations depending on their step. This sheds light on the speed of propagation of these
equations, notably in the “degenerated directions” of the subelliptic structure. First, for any γ ≥ 1,
we establish a resolvent estimate for the Baouendi-Grushin-type operator ∆γ = ∂2
y , which
x
has step γ + 1. We then derive consequences for the observability of the Schr´’odinger type equation
i ∂t u − (−∆γ)s u = 0 where s ∈ N. We identify three different cases: depending on the value of the
ratio (γ + 1)/s, observability may hold in arbitrarily small time, or only for sufficiently large times,
or even fail for any time. As a corollary of our resolvent estimate, we also obtain observability for
heat-type equations ∂t u + (−∆γ)s u = 0 and establish a decay rate for the damped wave equation
associated with ∆γ.

+ |x|2γ∂2

• In [40], we consider the evolution of a free quantum particle on the Grushin cylinder, under different
type of quantizations. In particular we are interested to understand if the particle can cross the
singular set, i.e., the set where the structure is not Riemannian. We consider intrinsic and extrinsic
quantizations, where the latter are obtained by embedding the Grushin structure isometrically
in R3 (with singularities). As a byproduct we provide formulas to embed the Grushin cylinder in
R3 that could be useful for other purposes. Such formulas are not global, but permit to study the
embedding arbitrarily close to the singular set. We extend these results to the case of α-Grushin
cylinders.

• In [47], we establish two results concerning the Quantum Limits (QLs) of some sub-Laplacians.
First, under a commutativity assumption on the vector fields involved in the definition of the sub-
Laplacian, we prove that it is possible to split any QL into several pieces which can be studied
separately, and which come from well-characterized parts of the associated sequence of eigen-
functions. Secondly, building upon this result, we study in detail the QLs of a particular family of
sub-Laplacians defined on products of compact quotients of Heisenberg groups. We express the
QLs through a disintegration of measure result which follows from a natural spectral decomposition
of the sub-Laplacian in which harmonic oscillators appear. Both results are based on the construc-
tion of an adequate elliptic operator commuting with the sub-Laplacian, and on the associated
joint spectral calculus. They illustrate the fact that, because of the possible high degeneracies in
the spectrum, the spectral theory of sub-Laplacians is very rich.

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• In [15], we consider surfaces embedded in a 3D contact sub-Riemannian manifold and the problem
of the finiteness of the induced distance (i.e., the infimum of the length of horizontal curves that
belong to the surface). Recently it has been proved that for a surface having the topology of a
sphere embedded in a tight co-orientable structure, the distance is always finite. In this paper we
study closed surfaces of genus larger than 1, proving that such surfaces can be embedded in such
a way that the induced distance is finite or infinite. We then study the structural stability of the
finiteness/not-finiteness of the distance.

• The relative heat content associated with a subset Ω ⊂ M of a sub-Riemannian manifold, is defined
as the total amount of heat contained in Ω at time t , with uniform initial condition on Ω, allow-
ing the heat to flow outside the domain. In the work [13], we obtain a fourth-order asymptotic
expansion in square root of t of the relative heat content associated with relatively compact non-
characteristic domains. Compared to the classical heat content that we studied in [Rizzi, Rossi - J.
Math. Pur. Appl., 2021], several difficulties emerge due to the absence of Dirichlet conditions at
the boundary of the domain. To overcome this lack of information, we combine a rough asymp-
totic for the temperature function at the boundary, coupled with stochastic completeness of the
heat semi-group. Our technique applies to any (possibly rank-varying) sub-Riemannian manifold
that is globally doubling and satisfies a global weak Poincaré inequality, including in particular
sub-Riemannian structures on compact manifolds and Carnot groups.

• In [22], we study the isoperimetric problem for anisotropic left-invariant perimeter measures on
R3, endowed with the Heisenberg group structure. The perimeter is associated with a left-invariant
norm φ on the horizontal distribution. We first prove a representation formula for the φ-perimeter
of regular sets and, assuming some regularity on φ and on its dual norm φ∗, we deduce a foliation
property by sub-Finsler geodesics of C 2-smooth surfaces with constant φ-curvature. We then prove
that the characteristic set of C 2-smooth surfaces that are locally extremal for the isoperimetric
problem is made of isolated points and horizontal curves satisfying a suitable differential equation.
Based on such a characterization, we characterize C 2-smooth φ-isoperimetric sets as the sub-
Finsler analogue of Pansu’s bubbles. We also show, under suitable regularity properties on φ,
that such sub-Finsler candidate isoperimetric sets are indeed C 2-smooth. By an approximation
procedure, we finally prove a conditional minimality property for the candidate solutions in the
general case (including the case where φ is crystalline).

7 Bilateral contracts and grants with industry

Participants:

Emmanuel Trélat, Veljko Askovic, Georgy Scholten.

7.1 Bilateral contracts with industry

Contract with MBDA (Palaiseau), 2021–2023. Subject: “Contrôle optimal pour la planification de tra-
jectoires et l’estimation des ensembles accessibles". Pariticpants: V. Askovic (MBDA & CAGE), E. Trélat
(coordinator).

7.2 Bilateral grants with industry

Grant by AFOSR (Air Force Office of Scientific Research), 2020–2023. Participants : Mohab Safey El Din
(LIP6), E. Trélat.

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8 Partnerships and cooperations

8.1 International research visitors

8.1.1 Visits of international scientists

Inria International Chair Andrei Agrachev (SISSA, Trieste, Italy) made two visits to CAGE (16/1–15/3
and 19/9–18/11) in the framework of his Inria International Chair 2020-2024.

Other international visits to the team Riccardo Adami (Politecnico di Torino, Italy), March.

8.2 National initiatives

8.2.1 ANR

• ANR TRECOS, for New Trends in Control and Stabilization: Constraints and non-local terms, co-
ordinated by Sylvain Ervedoza, University of Bordeaux. The ANR started in 2021 and runs up to
2025. TRECOS’ focus is on control theory for partial differential equations, and in particular models
from ecology and biology.

• ANR QUACO, for QUAntum COntrol: PDE systems and MRI applications, coordinated by Thomas
Chambrion, started in 2017 and finished in June 2023. Other partners: Burgundy University. QUACO
contributed to quantum control theory in two directions: improving the comprehension of the
dynamical properties of controlled quantum systems in infinite-dimensional state spaces, and
improving the efficiency of control algorithms for MRI.

• ANR/DFG CoRoMo for Efficient quantum control of molecular rotations – time and controllability,
2023–2025. The grant is co-coordinated by Ugo Boscain (CAGE) and Christiane Koch (Berlin). In this
project, we seek to elucidate the role of time in quantum control, using the important benchmark
of molecular rotations as testbed. We will leverage controllability analysis to tackle the role of time
in quantum control, combining physical intuition from the control of molecular rotations with
recent advances of mathematical methods.

• ANR EINSTEIN-PPF for Contraintes d’Einstein : passé’, présent et futur, coordinated by Philippe
Lefloch. Relying on a close collaboration between analysts and geometers, the ANR project is
aimed at advancing our knowledge of the analytic and geometric properties of Einstein spacetimes,
especially when the metrics under consideration have low regularity.

8.2.2 Other national initatives

• The Inria Exploratory Action “StellaCage” is supporting since Spring 2020 a collaboration between
CAGE, Yannick Privat (Inria team TONUS), and the startup Renaissance Fusion, based in Grenoble.
StellaCage approaches the problem of designing better stellarators (yielding better confinement,
with simpler coils, capable of higher fields) by combining geometrical properties of magnetic field
lines from the control perspective with shape optimization techniques.

• The 80 prime project BioSpeech (2023–2024), coordinated by Ugo Boscain, studies a bio-inspired
geometric model for speech sound reconstruction. It is a collaboration between mathematicians,
automatic control scientists, and linguists.

8.3 Regional initiatives

The Bourse Emergence(s) de la Ville de Paris “Morphométrie sous contrainte pour l’analyse de données
biologiques : un nouvel outil pour la communauté scientifique”, whose principal investigator is Barbara
Gris, runs from 2022 to 2025.

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9 Dissemination

9.1 Promoting scientific activities

9.1.1 Scientific events: organisation

• Ugo Boscain, Jean-Michel Coron, Kévin Le Balc’h, Mario Sigalotti, and Emmanuel Trélat are mem-
bers of the scientific committee of the Groupe de Travail Contrôle. Emmanuel Trélat is the main
organizer of this regular seminar.

Member of the organizing and scientific committees

• Ugo Boscain was organizer (together with Domenico D’Alessandro) of the triple session “Geometric
Control Theory with Quantum and Classical Applications” at the SIAM Conference on Control and
Its Applications, Philadelphia, USA, July.

• Ugo Boscain was organizer (together with Giovanni Marelli) of the CIMPA school “Contemporary

Geometry”. Windhoeck Namibia, January.

• Ugo Boscain and Mario Sigalotti were organizers (with D. Barilari, D. Prandi, L. Rizzi, Y. Sachkov, A.
Sarychev) of the conference “Geometry and Control in Cortona”, Palazzone, Cortona Italy, March.

• Barbara Gris was in the dans local organizing committee of the conference of the FoCM society.

• Kévin Le Balc’h was co-organizer of the workhsop “Contrôle, Stabilisation et EDP” in Rennes, June.

• Emmanuel Trélat is in the scientific committee of the next SMAI Mode conference, Lyon.

• Emmanuel Trélat was in the scientific committee of the conference “New Trends and Challenges in

Optimization Theory Applied to Space Engineering”, l’Aquila, Itay, December.

9.1.2 Journal

Member of the editorial boards

• Ugo Boscain is Associate editor of SIAM Journal on Control and Optimization and he is Correspond-

ing editor of the special section “Control of Quantum Mechanical Systems”.

• Ugo Boscain is Managing editor of Journal of Dynamical and Control Systems

• Jean-Michel Coron is Editor-in-chief of Comptes Rendus Mathématique

• Jean-Michel Coron is Associate editor of Journal of Evolution Equations

• Jean-Michel Coron is Associate editor of Asymptotic Analysis

• Jean-Michel Coron is Associate editor of ESAIM: Control, Optimisation and Calculus of Variations

• Jean-Michel Coron is Associate editor of Applied Mathematics Research Express

• Jean-Michel Coron is Associate editor of Advances in Differential Equations

• Jean-Michel Coron is Associate editor of Mathematics of Control, Signals, and Systems

• Jean-Michel Coron is Associate editor of Annales de l’IHP, Analyse non linéaire

• Mario Sigalotti is Associate editor of SIAM Journal on Control and Optimization

• Mario Sigalotti is Associate editor of ESAIM: Control, Optimisation and Calculus of Variations

• Mario Sigalotti is Associate editor of Journal on Dynamical and Control Systems

• Emmanuel Trélat is Editor-in-chief of ESAIM: Control, Optimisation and Calculus of Variations

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• Emmanuel Trélat is Associate editor of SIAM Review

• Emmanuel Trélat is Associate editor of Systems & Control Letters

• Emmanuel Trélat is Associate editor of Journal on Dynamical and Control Systems

• Emmanuel Trélat is Associate editor of Bollettino dell’Unione Matematica Italiana

• Emmanuel Trélat is Associate editor of ESAIM: Mathematical Modelling and Numerical Analysis

• Emmanuel Trélat is Editor of BCAM Springer Briefs

• Emmanuel Trélat is Associate editor of IEEE Transactions on Automatic Control

• Emmanuel Trélat is Associate editor of Journal of Optimization Theory and Applications

• Emmanuel Trélat is Associate editor of Mathematical Control & Related Fields

• Emmanuel Trélat is Associate editor of Mathematics of Control, Signals, and Systems

• Emmanuel Trélat is Associate editor of Optimal Control Applications and Methods

• Emmanuel Trélat is Associate editor of Advances in Continuous and Discrete Models: Theory and

Modern Applications

9.1.3 Invited talks

• Ugo Boscain was invited speaker at the Journée Colloquium de Mathématiques, Laboratoire de

Mathématiques d’Avignon.

• Ugo Boscain was invited speaker at ENS de Lyon, Workshop Defi EQIP 2023.

• Ugo Boscain was invited speaker at the conference “Optimization and Control in Burgundy”.

• Barbara Gris was invited speaker at the séminaire de modélisation mathématique en sciences de la

vie et santé (LAGA).

• Barbara Gris was invited speaker at the journée annuelle du groupe thématique SIGMA de la SMAI.

• Kévin Le Balc’h was invited speaker at the Workshop “Control and Related Fields”, University of

Sevilla, Spain.

• Kévin Le Balc’h was invited speaker at the Colloquium UNAM, Mexico City, Mexico.

• Kévin Le Balc’h was invited speaker at the Online seminar of Dortmund, Germany.

• Kévin Le Balc’h was invited speaker at at the Workshop EDP Cosy, Toulouse.

• Kévin Le Balc’h was invited speaker at the seminar of the numberical analysis and PDEs team,

Sevilla, Spain.

• Mario Sigalotti was invited speaker at the Workshop EDP-COSy, Toulouse.

• Mario Sigalotti was invited speaker at the seminar of the Math department of the Humboldt-

Universität zu Berlin, Germany.

• Emmanuel Trélat was plenary speaker at SCINDIS 2023, Wuppertal, Germany.

• Emmanuel Trélat was plenary speaker at SMAI 2023, Guadeloupe.

• Emmanuel Trélat was invited speaker at the conference “Control of Partial Differential Equations in

Hauts-de-France”, Valenciennes.

• Emmanuel Trélat was invited speaker at the Workshop EDP-COSy, Toulouse.

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Inria Annual Report 2023

• Emmanuel Trélat was invited speaker at the seminar MBDA, Le Plessis-Robinson.

• Emmanuel Trélat was invited speaker at Texas A& M, College Station.

• Emmanuel Trélat was invited speaker at the franco-corean weminar.

• Emmanuel Trélat was invited speaker at ENS Ker Lann.

• Emmanuel Trélat was invited speaker at Fe‘de‘ration Charles Hermite, Nancy.

• Emmanuel Trélat was invited speaker at the seminar of the Institut Jean Le Rond d’Alembert.

• Emmanuel Trélat was invited speaker at the seminar PDE, LJK, Grenoble.

9.1.4 Leadership within the scientific community

• Ugo Boscain is Délégueé Scientifique at INSMI in charge of interdisciplinarity and member of the

Comité de pilotage of the Mission pour les initiatives transverses et interdisciplinaires (MITI).

• Emmanuel Trélat is Head of the Laboratoire Jacques-Louis Lions (LJLL).

9.1.5 Scientific expertise

• Emmanuel Trélat is member of the conseil scientifique de la Fédération de Mathématiques de

CentraleSupelec.

• Emmanuel Trélat is member of the Advisory Board of the Department of Data Science, FAU (Erlan-

gen), Germany.

9.1.6 Research administration

• Kévin Le Balc’h is SMAI correspondent for the Laboratoire Jacques-Louis Lions.

• Emmanuel Trélat is member of the Bureau de comité des équipes-projets, Inria Paris center.

9.2 Teaching - Supervision - Juries

9.2.1 Teaching

• Ugo Boscain thought “ Geometric Control Theory” to PhD students at SISSA, Trieste, Italy.

• Ugo Boscain thought “Complements on sub-Riemannian geometry” at the CIMPA PhD school

“Contemporary Geometry”, Windhoeck Namibia.

• Ugo Boscain and Mario Sigalotti thought “Geometric control theory” at the M2 Mathématiques de

la Modélisation, Sorbonne Université.

• Barbara Gris was in charge of the supervision of projects for l3 students,Sorbonne Université.

• Kévin Le Balc’h thought Encadrement de leçons d’agrégation externe de mathématiques to M2

students at Sorbonne Université.

• Kévin Le Balc’h thought “Approximation des EDP elliptiques” to M1 students at Sorbonne Uni-

versité.

• Kévin Le Balc’h thought “Agrégation (analyse, probabilités)” to M2 students at Sorbonne Université.

• Kévin Le Balc’h thought “Analyse numérique” to L3 students at Sorbonne Université.

• Kévin Le Balc’h was the tutor of a M2 student at Sorbonne Université.

• Emmanuel Trélat thought “Contrôle en dimension finie et infinie” to M2 students at Sorbonne

Université

• Emmanuel Trélat thought “Optimisation numérique et sciences des données” to M1 students at

Sorbonne Université

Project CAGE

9.2.2 Supervision

19

• PhD: Veljko Askovic, “Aerial vehicle guidance problem by the Pontryagin Maximum Principle and
Hamilton Jacobi Bellman approach”, December 2023. Supervisors: Emmanuel Trélat and Hasnaa
Zidani (INSA, Rouen).

• PhD in progress: Kala Agbo Bidi, “Robust pest control strategies”. Supervisors: Luis Almeida and

Jean-Michel Coron.

• PhD in progress: Liangying Chen, “Sensitivity, Verification and Conjugate Times in Stochastic
Optimal Control”, started in 2021. Supervisors: Emmanuel Trélat and Xu Zhang (Chengdu, China).

• PhD in progress: Ruikang Liang, “The quantum speed limit in Quantum Control”, started in 2022.

Supervisors: Ugo Boscain and Mario Sigalotti.

• PhD in progress: Xiangyu Ma, “A bio-inspired geometric model for speech sound reconstruction”,

started in 2023. Supervisors: Ugo Boscain, Dario Prandi, and Giuseppina Turco.

• PhD in progress: Rayane Mouhli, “L’ontogénèse par grandes déformations”, started in 2023. Super-

visors: Barbara Gris and Irène Kaltenmark.

• PhD in progress: Robin Roussel, “Magnetic field lines and confinement in stellarators: a Hamilto-

nian perspective”, started in 2021. Supervisors: Ugo Boscain and Mario Sigalotti.

• PhD in progress: Lucia Tessarolo, “Sub- Riemannian geometry and pinwheels”, started in 2023.

Supervisor: Ugo Boscain.

• Kévin Le Balc’h was member of the comités de suivi of the PhD theses of Cristobal Loboya and Ivan

Hasenohr.

9.2.3 Juries

• Mario Sigalotti was member of the PhD jury of Gautier Roman, Sorbonne Universite‘.

• Mario Sigalotti and Emmanuel Trélat were members of the PhD jury of Veljko Askovic, Sorbonne

Universite‘.

• Emmanuel Trélat was president of the HDR jury of Ihab Haidar, Univiversité de Cergy.

• Emmanuel Trélat was member of the HDR jury of C. J. Silva, University of Aveiro, Portugal.

• Emmanuel Trélat was member of the HDR jury of Amaury Hayat, Université Paris-Dauphine.

• Emmanuel Trélat was member of the PhD jury of R. Pre‘bet, Sorbonne Universite‘.

• Emmanuel Trélat was referee and member of the PhD jury of R. Loyer, Université du Littoral.

• Emmanuel Trélat was member of the PhD jury of M. Harakeh, Université d’Orle‘ans.

• Emmanuel Trélat was referee and member of the PhD jury of A. Bouali, Université d’Avignon.

• Emmanuel Trélat was referee and member of the PhD jury of A. Herasimenka, Université Côte

d’Azur.

• Emmanuel Trélat was referee and member of the PhD jury of L. Mascolo, Politecnico di Torino,

Italy.

• Emmanuel Trélat was referee and member of the PhD jury of H. Me‘nou, Ecole des Mines de Paris.

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Inria Annual Report 2023

10 Scientific production

10.1 Major publications

[1] D. Barilari, Y. Chitour, F. Jean, D. Prandi and M. Sigalotti. ‘On the regularity of abnormal minimizers
for rank 2 sub-Riemannian structures’. In: Journal de Mathématiques Pures et Appliquées 133
(2020), pp. 118–138. DOI: 10.1016/j.matpur.2019.04.008. URL: https://hal.archives-ou
vertes.fr/hal-01757343.

[2] R. Bonalli, B. Hérissé and E. Trélat. ‘Optimal Control of Endo-Atmospheric Launch Vehicle Systems:
Geometric and Computational Issues’. In: IEEE Transactions on Automatic Control 65.6 (2020),
pp. 2418–2433. DOI: 10.1109/tac.2019.2929099. URL: https://hal.archives-ouvertes.f
r/hal-01626869.

[3] Y. Colin de Verdìère, L. Hillairet and E. Trélat. Spectral asymptotics for sub-Riemannian Laplacians.

5th Dec. 2022. URL: https://hal.archives-ouvertes.fr/hal-03885610.

[4]

[5]

[6]

[7]

J.-M. Coron, A. Hayat, S. Xiang and C. Zhang. ‘Stabilization of the linearized water tank system’.
In: Archive for Rational Mechanics and Analysis 244.3 (2022), pp. 1019–1097. URL: https://hal
.archives-ouvertes.fr/hal-03161523.

J.-M. Coron, F. Marbach and F. Sueur. ‘Small-time global exact controllability of the Navier-
Stokes equation with Navier slip-with-friction boundary conditions’. In: Journal of the European
Mathematical Society 22.5 (May 2020), pp. 1625–1673. DOI: 10.4171/JEMS/952. URL: https://h
al.archives-ouvertes.fr/hal-01422161.

J.-M. Coron and H.-M. Nguyen. ‘Optimal time for the controllability of linear hyperbolic systems
in one dimensional space’. In: SIAM Journal on Control and Optimization 57.2 (5th Apr. 2019),
pp. 1127–1156. DOI: 10.1137/18M1185600. URL: https://hal.archives-ouvertes.fr/hal-
01952134.

S. Ervedoza, K. Le Balc’H and M. Tucsnak. ‘Reachability results for perturbed heat equations’. In:
Journal of Functional Analysis 283.10 (15th Nov. 2022). URL: https://hal.archives-ouvertes
.fr/hal-03380745.

[8] M. Leibscher, E. Pozzoli, C. Pérez, M. Schnell, M. Sigalotti, U. Boscain and C. P. Koch. ‘Full quantum
control of enantiomer-selective state transfer in chiral molecules despite degeneracy’. In: Com-
munications Physics (6th May 2022). DOI: 10.1038/s42005-022-00883-6. URL: https://hal
.inria.fr/hal-02972059.

[9] O. Öktem, B. Gris and C. Chen. ‘Image reconstruction through metamorphosis’. In: Inverse Prob-
lems 36 (2020). DOI: 10.1088/1361-6420/ab5832. URL: https://hal.archives-ouvertes.f
r/hal-01773633.

[10] Y. Privat, R. Robin and M. Sigalotti. ‘Optimal shape of stellarators for magnetic confinement fusion’.
In: Journal de Mathématiques Pures et Appliquées (2022). DOI: 10.1016/j.matpur.2022.05.005.
URL: https://hal.inria.fr/hal-03472623.

[11] R. Robin, N. Augier, U. Boscain and M. Sigalotti. ‘Ensemble qubit controllability with a single
control via adiabatic and rotating wave approximations’. In: Journal of Differential Equations 318
(5th May 2022). DOI: 10.1016/j.jde.2022.02.042. URL: https://hal.archives-ouvertes
.fr/hal-02504532.

10.2 Publications of the year

International journals

[12] A. Agrachev and P. Nurowski. ‘Ants and bracket generating distributions in dimension 5 and 6’. In:

Automatica 147 (2023). URL: https://hal.science/hal-04032758.

[13] A. Agrachev, L. Rizzi and T. Rossi. ‘Relative heat content asymptotics for sub-Riemannian mani-

folds’. In: Analysis & PDE (2023). URL: https://hal.science/hal-03372680.

Project CAGE

21

[14] B. Bonnet, C. Cipriani, M. Fornasier and H. Huang. ‘A Measure Theoretical Approach to the Mean-
field Maximum Principle for Training NeurODEs’. In: Nonlinear Analysis: Theory, Methods and
Applications 227 (2023), p. 113161. DOI: 10.1016/j.na.2022.113161. URL: https://hal.scie
nce/hal-03289521.

[15] U. Boscain and E. Bellini. ‘Surfaces of genus g ≥ 1 in 3D contact sub-Riemannian manifolds’. In:
ESAIM: Control, Optimisation and Calculus of Variations 29 (8th Nov. 2023), p. 79. DOI: 10.1051
/cocv/2023072. URL: https://hal.science/hal-04307729.

[16] F. W. Chaves-Silva, E. Fernández-Cara, K. Le Balc’h, J. Machado and S. Diego A. ‘Global Controllab-
ility of the Boussinesq System with Navier-Slip-with-Friction and Robin Boundary Conditions’. In:
SIAM Journal on Control and Optimization 61.2 (24th Mar. 2023), pp. 484–510. DOI: 10.1137/21
M1425566. URL: https://hal.science/hal-04364123.

[17] Y. Chitour, S. Fueyo, G. Mazanti and M. Sigalotti. ‘Hautus-Yamamoto criteria for approximate and
exact controllability of linear difference delay equations’. In: Discrete and Continuous Dynamical
Systems - Series A 43.9 (Sept. 2023), pp. 3306–3337. DOI: 10.3934/dcds.2023049. URL: https:
//hal.science/hal-03827918.

[18] Y. Chitour, I. I. Haidar, P. Mason and M. Sigalotti. ‘Upper and lower bounds for the maximal
Lyapunov exponent of singularly perturbed linear switching systems’. In: Automatica 155 (2023),
p. 111151. DOI: 10.1016/j.automatica.2023.111151. URL: https://hal.science/hal-03
668881.

[19] Y. Chitour, G. Mazanti, P. Monmarché and M. Sigalotti. ‘On the gap between deterministic and
probabilistic Lyapunov exponents for continuous-time linear systems’. In: Electronic Journal of
Probability 28 (2023), Paper No. 43, 39 pp. DOI: 10.1214/23-EJP932. URL: https://hal.scien
ce/hal-03478271.

[20]

J.-M. Coron, S. Xiang and P. Zhang. ‘On the global approximate controllability in small time of
semiclassical 1-D Schrödinger equations between two states with positive quantum densities’. In:
Journal of Differential Equations 345 (5th Feb. 2023), pp. 1–44. DOI: 10.1016/j.jde.2022.11.0
21. URL: https://hal.science/hal-03408056.

[21] S. Ervedoza and K. Le Balc’h. ‘Cost of observability inequalities for elliptic equations in 2-d
with potentials and applications to control theory’. In: Communications in Partial Differential
Equations 48.4 (10th Apr. 2023), pp. 623–677. DOI: 10.1080/03605302.2023.2190526. URL:
https://hal.science/hal-03616317.

[22] V. Franceschi, R. Monti, A. Righini and M. Sigalotti. ‘The isoperimetric problem for regular and
crystalline norms in H1’. In: The Journal of Geometric Analysis (2023). DOI: 10.1007/s12220-022
-01045-4. URL: https://hal.science/hal-02905108.

[23]

S. Fueyo, G. Mazanti, I. Boussaada, Y. Chitour and S.-I. Niculescu. ‘On the pole placement of scalar
linear delay systems with two delays’. In: IMA Journal of Mathematical Control and Information
40.1 (17th Feb. 2023), pp. 81–105. DOI: 10.1093/imamci/dnad001. URL: https://hal.science
/hal-03669644.

[24] A. Hayat, B. Piccoli and S. Truong. ‘Dissipation of traffic jams using a single autonomous vehicle
on a ring road’. In: SIAM Journal on Applied Mathematics 83.3 (1st Jan. 2023). DOI: 10.1137/21M1
414346. URL: https://hal.science/hal-03354282.

[25] V. Hernández-Santamaría, K. Le Balc’h and L. Peralta. ‘Global null-controllability for stochastic
semilinear parabolic equations’. In: Annales de l’Institut Henri Poincaré C, Analyse non linéaire
(13th Jan. 2023), pp. 1415–1455. DOI: 10.4171/AIHPC/69. URL: https://hal.science/hal-03
935065.

[26] E. Humbert, Y. Privat and E. Trélat. ‘Quantum Limits on product manifolds’. In: Indiana University
Mathematics Journal 72.2 (2023), pp. 757–783. DOI: 10.1512/iumj.2023.72.9755. URL: https:
//hal.science/hal-03562358.

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[27] C. Letrouit. ‘Catching all geodesics of a manifold with moving balls and application to control-
lability of the wave equation’. In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
XXIV (2023), p. 15. DOI: 10.2422/2036-2145.202010_004. URL: https://hal.science/hal-
02102135.

[28] C. Letrouit and C. Sun. ‘Observability of Baouendi-Grushin-Type Equations Through Resolvent
Estimates’. In: Journal of the Institute of Mathematics of Jussieu 22.2 (2023), pp. 541–579. DOI:
10.1017/S1474748021000207. URL: https://hal.science/hal-02964024.

[29] P. Mason, Y. Chitour and M. Sigalotti. ‘On universal classes of Lyapunov functions for linear
switched systems’. In: Automatica 155 (2023), p. 111155. DOI: 10.1016/j.automatica.2023.11
1155. URL: https://hal.science/hal-03753540.

[30] E. Trélat. ‘Linear turnpike theorem’. In: Mathematics of Control, Signals, and Systems 35.3 (2023),

pp. 685–739. URL: https://hal.science/hal-02978505.

International peer-reviewed conferences

[31] K. Agbo Bidi, J.-M. Coron, A. Hayat and N. Lichtlé. ‘Reinforcement Learning in Control Theory:
A New Approach to Mathematical Problem Solving’. In: The 3rd Workshop on Mathematical
Reasoning and AI at NeurIPS’23. 3rd Workshop on Mathematical Reasoning and AI at NeurIPS’23.
New Orleans (LA), United States, 15th Dec. 2023. URL: https://hal.science/hal-04250601.

Reports & preprints

[32] K. Agbo Bidi, L. Almeida and J.-M. Coron. Global stabilization of sterile insect technique model by

feedback laws. 1st July 2023. URL: https://hal.science/hal-04147979.

[33] A. Agrachev. "Good Lie Brackets" for Control Affine Systems. 22nd May 2023. URL: https://inria

.hal.science/hal-04104558.

[34] A. Agrachev, S. Baranzini and I. Beschastnyi. Index theorems for graph-parametrized optimal

control problems. 24th Jan. 2022. URL: https://inria.hal.science/hal-04032698.

[35] A. A. Agrachev and M. Motta. Lyapunov Exponents of Linear Switched Systems. 18th Dec. 2023.

URL: https://inria.hal.science/hal-04353841.

[36] V. Askovic, E. Trélat and H. Zidani. Linear quadratic optimal control turnpike in finite and infinite
dimension: two-term expansion of the value function. 22nd Dec. 2023. URL: https://hal.scien
ce/hal-04361557.

[37] V. Askovic, E. Trélat and H. Zidani. Two-term large-time asymptotic expansion of the value function
for dissipative nonlinear optimal control problems. 2023. URL: https://hal.science/hal-043
45255.

[38] K. L. Balc’H and J. Martin. Global stabilization of the cubic defocusing nonlinear Schrödinger

equation on the torus. 16th Oct. 2023. URL: https://hal.science/hal-04296638.

[39] L. Baratchart, S. Fueyo and J.-B. Pomet. Exponential stability of linear periodic difference-delay

[40]

equations. 2023. URL: https://inria.hal.science/hal-03500720.
I. Beschastnyi, U. Boscain, D. Cannarsa and E. Pozzoli. Embedding the Grushin Cylinder in R3and
Schroedinger evolution. 3rd Apr. 2023. URL: https://hal.science/hal-04057223.

[41] L. Bourdin and E. Trélat. Convergence in nonlinear optimal sampled-data control problems. 2023.

URL: https://hal.science/hal-03975698.

[42] Y. Chitour, S. Fueyo, G. Mazanti and M. Sigalotti. Approximate and exact controllability criteria for
linear one-dimensional hyperbolic systems. 4th Oct. 2023. URL: https://inria.hal.science/h
al-04228797.

[43] W. Gerner. Existence of optimal domains for the helicity maximisation problem among domains
satisfying a uniform ball condition. 23rd May 2023. URL: https://hal.science/hal-04103519.

[44] W. Gerner. Properties of the Biot-Savart operator acting on surface currents. 6th Nov. 2023. URL:

https://hal.science/hal-04271879.

Project CAGE

23

[45] K. Le Balc’h and J. Martin. Observability estimates for the Schrödinger equation in the plane with
periodic bounded potentials from measurable sets. 14th Apr. 2023. URL: https://hal.science/h
al-04069809.

[46] M. Leibscher, E. Pozzoli, A. Blech, M. Sigalotti, U. Boscain, U. Boscain and C. P. Koch. Quantum
control of ro-vibrational dynamics and application to light-induced molecular chirality. 17th Oct.
2023. URL: https://inria.hal.science/hal-04254059.

[47] C. Letrouit. Quantum limits of sub-Laplacians via joint spectral calculus. 2nd Apr. 2023. URL:

https://hal.science/hal-02886099.

[48] R. Liang, U. Boscain and M. Sigalotti. Controllability of quantum systems having weakly conically

connected spectrum. 22nd Oct. 2023. URL: https://hal.science/hal-04174206.

[49] E. Molina, P. Martinon, P. Martinon and H. Rámirez. Optimal control approaches for Open Pit

planning. 22nd Mar. 2023. URL: https://hal.science/hal-03588436.

[50] C. Pouchol, E. Trélat and C. Zhang. Approximate control of parabolic equations with on-off shape
controls by Fenchel duality. 11th Dec. 2023. URL: https://hal.science/hal-03889865.

[51] E. Trélat. Control in finite and infinite dimension. 22nd Dec. 2023. URL: https://hal.science

/hal-04361042.

10.3 Cited publications

[52] A. Agrachev, U. Boscain, J.-P. Gauthier and F. Rossi. ‘The intrinsic hypoelliptic Laplacian and
its heat kernel on unimodular Lie groups’. In: J. Funct. Anal. 256.8 (2009), pp. 2621–2655. DOI:
10.1016/j.jfa.2009.01.006. URL: https://doi.org/10.1016/j.jfa.2009.01.006.

[53] A. A. Agrachev and Y. L. Sachkov. Control theory from the geometric viewpoint. Vol. 87. Encyclopae-
dia of Mathematical Sciences. Control Theory and Optimization, II. Springer-Verlag, Berlin, 2004,
pp. xiv+412. DOI: 10.1007/978-3-662-06404-7. URL: https://doi.org/10.1007/978-3-6
62-06404-7.

[54] L. Ambrosio and P. Tilli. Topics on analysis in metric spaces. Vol. 25. Oxford Lecture Series in

Mathematics and its Applications. Oxford University Press, Oxford, 2004, pp. viii+133.

[55] S. Arguillère, E. Trélat, A. Trouvé and L. Younes. ‘Shape deformation analysis from the optimal
control viewpoint’. In: J. Math. Pures Appl. (9) 104.1 (2015), pp. 139–178. DOI: 10.1016/j.matpur
.2015.02.004. URL: https://doi.org/10.1016/j.matpur.2015.02.004.

[56] T. Bayen. ‘Analytical parameterization of rotors and proof of a Goldberg conjecture by optimal
control theory’. In: SIAM J. Control Optim. 47.6 (2008), pp. 3007–3036. DOI: 10.1137/070705325.

[57] M. Benaim, S. Le Borgne, F. Malrieu and P.-A. Zitt. ‘Qualitative properties of certain piecewise
deterministic Markov processes’. In: Ann. Inst. Henri Poincaré Probab. Stat. 51.3 (2015), pp. 1040–
1075. DOI: 10.1214/14-AIHP619. URL: https://doi.org/10.1214/14-AIHP619.

[58] B. Berret, C. Darlot, F. Jean, T. Pozzo, C. Papaxanthis and J. P. Gauthier. ‘The inactivation principle:
mathematical solutions minimizing the absolute work and biological implications for the planning
of arm movements’. In: PLoS Comput. Biol. 4.10 (2008), e1000194, 25. DOI: 10.1371/journal.pc
bi.1000194. URL: https://doi.org/10.1371/journal.pcbi.1000194.

[59] A. Bonfiglioli, E. Lanconelli and F. Uguzzoni. Stratified Lie groups and potential theory for their
sub-Laplacians. Springer Monographs in Mathematics. Springer, Berlin, 2007, pp. xxvi+800.

[60] B. Bonnard, L. Faubourg and E. Trélat. Mécanique céleste et contrôle des véhicules spatiaux. Vol. 51.
Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer-Verlag, Berlin,
2006, pp. xiv+276.

[61] U. Boscain, R. A. Chertovskih, J. P. Gauthier and A. O. Remizov. ‘Hypoelliptic diffusion and human
vision: a semidiscrete new twist’. In: SIAM J. Imaging Sci. 7.2 (2014), pp. 669–695. DOI: 10.1137/1
30924731.

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[62] U. Boscain, F. Chittaro, P. Mason and M. Sigalotti. ‘Adiabatic control of the Schroedinger equation
via conical intersections of the eigenvalues’. In: IEEE Trans. Automat. Control 57.8 (2012), pp. 1970–
1983.

[63] U. Boscain, J. Duplaix, J.-P. Gauthier and F. Rossi. ‘Anthropomorphic image reconstruction via
hypoelliptic diffusion’. In: SIAM J. Control Optim. 50.3 (2012), pp. 1309–1336. DOI: 10.1137/1108
2405X.

[64] R. W. Brockett. ‘System theory on group manifolds and coset spaces’. In: SIAM J. Control 10 (1972),

pp. 265–284.

[65] F. Bullo and A. D. Lewis. Geometric control of mechanical systems. Vol. 49. Texts in Applied Math-
ematics. Modeling, analysis, and design for simple mechanical control systems. Springer-Verlag,
New York, 2005, pp. xxiv+726. DOI: 10.1007/978-1-4899-7276-7.

[66] T. Chambrion, P. Mason, M. Sigalotti and U. Boscain. ‘Controllability of the discrete-spectrum
Schrödinger equation driven by an external field’. In: Ann. Inst. H. Poincaré Anal. Non Linéaire
26.1 (2009), pp. 329–349. DOI: 10.1016/j.anihpc.2008.05.001. URL: https://doi.org/10
.1016/j.anihpc.2008.05.001.

[67] G. Citti and A. Sarti. ‘A cortical based model of perceptual completion in the roto-translation
space’. In: J. Math. Imaging Vision 24.3 (2006), pp. 307–326. DOI: 10.1007/s10851-005-3630-2.
URL: http://dx.doi.org/10.1007/s10851-005-3630-2.

[68] F. Colonius and G. Mazanti. ‘Decay rates for stabilization of linear continuous-time systems with

random switching’. In: Math. Control Relat. Fields (2019).

[69]

[70]

[71]

J.-M. Coron. Control and nonlinearity. Vol. 136. Mathematical Surveys and Monographs. American
Mathematical Society, Providence, RI, 2007, pp. xiv+426.

J.-M. Coron. ‘Global asymptotic stabilization for controllable systems without drift’. In: Math.
Control Signals Systems 5.3 (1992), pp. 295–312. DOI: 10.1007/BF01211563. URL: https://doi
.org/10.1007/BF01211563.

J.-M. Coron. ‘On the controllability of nonlinear partial differential equations’. In: Proceedings
of the International Congress of Mathematicians. Volume I. Hindustan Book Agency, New Delhi,
2010, pp. 238–264.

[72] D. D’Alessandro. Introduction to quantum control and dynamics. Chapman & Hall/CRC Ap-
plied Mathematics and Nonlinear Science Series. Chapman & Hall/CRC, Boca Raton, FL, 2008,
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[73] M. Fliess, J. Lévine, P. Martin and P. Rouchon. ‘Flatness and defect of non-linear systems: intro-
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<scratchpad>
- Main topic: Research Centre CAGE (Control and Geometry)
- Key points: Control theory, applied mathematics, computation and simulation, optimization and control of dynamic systems
- Structure: The document is organized into sections, including Project-Team, Activity Report, Contents, Highlights of the Year, New Results, and Dissemination
- Potential artifacts to ignore: Links, HTML tags, web-related elements
</scratchpad>

<final_summary>
The Research Centre CAGE (Control and Geometry) is a collaboration between Inria Paris Centre, Sorbonne University, CNRS, and other partners. The centre focuses on control theory, applied mathematics, and computation and simulation, with a specific emphasis on optimization and control of dynamic systems. The research program covers various domains, including quantum control, stability and stabilization, motion planning, and geometric models for vision and sub-Riemannian geometry. The centre has achieved significant results in these areas, including new controllability estimates for quantum systems, stability and stabilization of control and hybrid systems, and motion planning and optimal control algorithms. The centre's work has been recognized with several awards, including the Brockett-Willems Outstanding Paper Award and the Prix solennel de thèse de la chancellerie de Paris.
The Research Centre CAGE (Control and Geometry) is a collaboration between Inria Paris Centre, Sorbonne University, CNRS, and other partners. The centre focuses on control theory, applied mathematics, and computation and simulation, with a specific emphasis on optimization and control of dynamic systems. The research program covers various domains, including quantum control, stability and stabilization, motion planning, and geometric models for vision and sub-Riemannian geometry. The centre has achieved significant results in these areas, including new controllability estimates for quantum systems, stability and stabilization of control and hybrid systems, and motion planning and optimal control algorithms. The centre's work has been recognized with several awards, including the Brockett-Willems Outstanding Paper Award and the Prix solennel de thèse de la chancellerie de Paris.