RESEARCH CENTRE

Inria Centre
at the University of Lille

2023
ACTIVITY REPORT

IN PARTNERSHIP WITH:

Ecole Centrale de Lille, Université de Lille

Project-Team

VALSE

Finite-time control and estimation for
distributed systems

IN COLLABORATION WITH: Centre de Recherche en Informatique, Signal
et Automatique de Lille

DOMAIN

Applied Mathematics, Computation and
Simulation

THEME

Optimization and control of dynamic
systems

Contents

Project-Team VALSE

1 Team members, visitors, external collaborators

2 Overall objectives

3 Research program

4 Application domains

5 Social and environmental responsibility

6 Highlights of the year

7 New software, platforms, open data

7.1 New software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 HCS Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2

3

3

4

6

6

7
7
7

8 New results

8
8
8.1 Analysis and design of homogeneous and finite-time stable systems . . . . . . . . . . . . . .
8
8.2 Analysis and design for time-delay systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
8.3 Discretisation of homogeneous systems
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4 Homogenization through controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
8.5 Control and estimation for Persidskii systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
8.6 Control of robotic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
8.7 Estimation under communication constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.8 Synchronization and multistability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

9 Bilateral contracts and grants with industry

12
9.1 Bilateral contracts with industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

10 Partnerships and cooperations

10.2 International research visitors

12
10.1 International initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
10.1.1 Participation in other International Programs . . . . . . . . . . . . . . . . . . . . . . . 12
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
10.2.1 Visits of international scientists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
10.3 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
10.3.1 ANR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
10.4 Regional initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

11 Dissemination

14
11.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
11.1.1 Scientific events: organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
11.1.2 Journal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
11.1.3 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
11.1.4 Leadership within the scientific community . . . . . . . . . . . . . . . . . . . . . . . . 15
11.1.5 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
11.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
11.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
11.2.2 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
11.3 Popularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
11.3.1 Internal or external Inria responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . 16
11.3.2 Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

12 Scientific production

12.1 Publications of the year
12.2 Cited publications

16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Project VALSE

1

Project-Team VALSE

Creation of the Project-Team: 2019 November 01

Keywords

Computer sciences and digital sciences

A5.9.2. – Estimation, modeling

A6.4.1. – Deterministic control

A6.4.4. – Stability and Stabilization

A6.4.5. – Control of distributed parameter systems

A9.5. – Robotics

Other research topics and application domains

B1.1.8. – Mathematical biology

B2.1. – Well being

B5.6. – Robotic systems

B7.2.1. – Smart vehicles

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Denis Efimov [Team leader, INRIA, Senior Researcher, HDR]

• Jin Gyu Lee [INRIA, ISFP]

• Andrey Polyakov [INRIA, Researcher, HDR]

• Rosane Ushirobira [INRIA, Researcher, HDR]

Post-Doctoral Fellow

• Jesus Mendoza Avila [INRIA, until Nov 2023]

PhD Students

• Mohamed Yassine Arkhis [INRIA, from Oct 2023]

• Mericel Ayamou [UNIV LILLE]

• Mahugnon Dadjo [INRAE]

• Min Li [CSC Scholarship]

• Danilo Rodrigues De Lima [INRIA]

• Yu Zhou [CSC Scholarship]

Technical Staff

• Gerald Dherbomez [CNRS, Engineer]

Administrative Assistant

• Lucille Leclercq [INRIA, from Feb 2023]

Visiting Scientists

• Leonid Fridman [UNAM, until Jan 2023]

• Ariana Gutierrez [IT Laguna, from Aug 2023 until Oct 2023]

• Ankit Kumar [IIT Delhi, from Mar 2023 until May 2023]

• Manuel Mera [Instituto Politécnico Nacional, from Aug 2023 until Sep 2023]

• Jose Antonio Ortega [UNAM, from Aug 2023 until Oct 2023]

• Hector Rios Barajas [IT Laguna, from Aug 2023 until Sep 2023]

Project VALSE

3

2 Overall objectives

The Valse team studies the estimation and control problems arising in the analysis and the design of
distributed, uncertain, and interconnected dynamical systems:

• Using the concepts of finite-time/fixed-time/hyperexponential convergence and stability, the main
idea is to separate and hierarchize in time the control and estimation processes, which are distrib-
uted in space. This greatly simplifies their analysis and the design for large-scale solutions.

• The main areas of investigation and application are the Internet of Things (IoT) and Cyber-Physical

Systems (CPS).

• The team aims to draw up algorithms for decentralized finite-time control and estimation. The
methodology to be developed includes extensions of the theory of homogeneous systems and of
finite-time/fixed-time/hyperexponential convergence and stability notions. Particular attention is
given to applications in real-world scenarios.

• It is a joint proposal with the CNRS CRIStAL UMR 9189.

3 Research program

The Valse team works in the domains of control science: dynamical systems, stability analysis, estimation,
and automatic control. Our developments are focused on the theoretical and applied aspects related to
the control and estimation of large-scale multi-sensor and multi-actuator systems based on the use of the
theories of finite-time/fixed-time/hyperexponential convergence and homogeneous systems. The Lyapunov
function method and other methods of analysis of dynamical systems form a basis for the studies in the
Valse team.

The key idea of the research program for the team is that a fast (non-asymptotic) convergence of the
regulation and estimation errors increases the reliability of intelligent distributed actuators and sensors
in complex scenarios, such as interconnected cyber-physical systems (CPSs).

The expertise of Valse’s members in theoretical developments of control and estimation theory
(finite-time control and estimation algorithms in centralized context [80, 67, 77, 75, 72], homogeneity
framework for differential equations [76, 66, 65, 71, 69, 81, 78], time-delay systems [68, 70, 84], distributed
systems [79] and algebraic-based methods for estimation [82, 83]) is an essential ingredient to achieve
our objective.

The generic chart of different goals and tasks included in the scientific work program of Valse and
interrelations between them are presented in Fig. 1. We have selected three main objectives to pursue
with the related tasks to fulfill:

• The first objective is to design control and estimation solutions for CPS and IoT, which is the

principal aim of Valse. It will contain the main outcomes of our research.

• The second objective is more theoretical and needed to make the basement for our design and

analysis parts in the last goal.

• The third objective deals with applications, which will drive the team and motivate the theoretical

studies and selected design performances.

All these objectives are interconnected: from a particular problem in an IoT application, it is planned to
design control or estimation algorithms, leading to the development of theoretical tools; and vice versa, a
new theoretical advance can provide a possibility for the development of novel tools which can be used
in applications.

To explain our motivation: why use finite time? Applying any method for control/estimation has
a price in terms of its advantages and disadvantages. There is no universal framework that is the best
always and everywhere. Finite-time may appear as a luxurious property for a physical system, requiring
nonlinear tools. Of course, if an asymptotic convergence and a linear model are enough for solving a
given problem, then there is no reason to develop something else. However, most of the present problems

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Inria Annual Report 2023

Figure 1: Structure of the objectives and tasks treated in Valse

Figure 2: The valvometer used in the ANR project WaQMoS

in CPS and IoT are nonlinear (i.e., they have various local behaviors that cannot be collected in only one
linear model). Design and analysis of various local linearized models and solutions are luxurious, too.
The theory of homogeneity can go beyond linearity, offering many new features while not appearing as
severe as other nonlinear tools and having almost all hints of the linear framework. Suppose that, thanks
to the homogeneity theory, finite-time/fixed-time can be obtained with little difficulty while adding the
bonuses of stronger robustness and faster convergence compared to the linear case? We are convinced
that the price of going beyond linear control and estimation can be strongly dropped by maturing the theory
of homogeneity and finite/fixed-time convergence. We are also convinced that it will be compensated in
terms of robustness and speed, which can be demanded in the new areas of application such as IoT for
example.

4 Application domains

An objective of the team is the application of the developed control and estimation algorithms for different
scenarios in IoT or CPSs. Participation in various potential applications allows the Valse team to better
understand the features of CPSs and their required performances, and to properly formulate the control
and estimation problems that must be solved. Here is a list of ongoing, past and potential applications
addressed by the team:

• smart bivalve-based biosensor for water quality monitoring (ANR project WaQMoS, the developed
sensor is shown in Fig. 2): in living beings, the presence of persistent external perturbations may be
difficult to measure, and important model uncertainties render the application of conventional
techniques complicated; another issue for estimation is the consensus-seeking between animals
for contamination detection [63];

1. Finite-time control and estimation in distributed CPS •variety of mathematical models •interconnection & dimension •certification & guarantee  2. Development of theoretical background•homogeneity •finite-time/fixed-time/hyperexponential  convergence •Lyapunov characterisations •robustness •connectivity constraints •algebraic methods 3. Applications in IoT and CPS•estimation biosensors: oysters, wearables, … HCI •control and estimation flow control ControlHub, robots (blimps, …) Project VALSE

5

Figure 3: Blimp and quadrotor robots

Figure 4: Particle Image Velocimetry on flow control for an Ahmed body (LAMIH wind tunnel)

• control and estimation for flying vehicles, e.g. quadrotors or blimps given in Fig. 3: the nonlinearity
of the model and its uncertainty coupled with important aerodynamic perturbations have to be
compensated by fast (finite- or fixed-time) and robust control and estimation algorithms;

• human behavior modeling and identification with the posterior design of algorithms for human-
computer interaction (HCI, with the Inria team LOKI): robust finite-time differentiators demon-
strate good estimation capabilities needed for prediction in this application [83, 64];

• human physiological characteristics estimation (like emotion detection, galvanic skin response
filtering, fatigue evaluation in collaborations with Neotrope and Ellcie Healthy): intelligent robust
filtering and finite-time distributed estimation are key features in these scenarios;

• path planning for autonomous vehicles taking into account the behavior of humans (with the
Inria team SCOOL): application of interval and finite-time adaptive estimation and prediction
techniques allows for treating the uncertainty of the environment by reducing the computational
complexity of reinforcement learning [74]1;

• flow control [73]: the case of control and estimation of a distributed-parameter system with very
fast and uncertain dynamics, where finite-time solutions developed by Valse are necessary (an
example of results is given in Fig. 4);

• control of bioreactors (in the framework of IPL COSY): here again, the problem is an important
uncertainty of the model, which can be handled by robust sliding mode control algorithms, or by
applying adaptive finite-time estimation and identification tools;

1The examples of interval prediction algorithm application can be consulted here.

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Inria Annual Report 2023

It is worth highlighting a widespread distribution of various scientific domains in the list of applic-
ations for the team given above. Such interdisciplinarity for Valse is unsurprising since control theory
is a science of systems whose interest today is, by nature, to interface with other disciplines and their
fields of application. This is also well aligned with the domain of CPSs, which by its origin requires
multidisciplinary competencies.

5 Social and environmental responsibility

Activities of the team related with social responsibility:

• Engaging in outreach programs to promote mathematics education and awareness in local com-

munities: Rosane Ushirobira participes in the work of CIMPA

• Collaborating with educational institutions to support the development of math skills for young
generation: Rosane Ushirobira made several CHICHE sessions in high schools of Lille and metro-
politan area

• Participating in mentorship programs to encourage underrepresented groups to pursue careers in
mathematics and related fields: Rosane Ushirobira organized the days of young girls in informatics
and mathematics (RJMI)

• Contributing to interdisciplinary research that addresses societal challenges, such as healthcare, by
applying mathematical modeling and analysis: a new ANR project NOCIME has been accepted with
participation of the team on analysis of epidimiological models, in addition, there are publications
on this subject

• Mentoring and supporting early-career researchers to foster a diverse and inclusive research

community

Activities of the team related with environmental responsibility:

• Developing mathematical models and the methods for their design and analysis to support sus-

tainable energy systems: ANR project SyNPiD devoted to this issue

• Collaborating with environmental scientists, engineers, and policymakers to provide mathemat-
ical insights and solutions for environmental challenges and their mitigations: a PhD student is
supervised with INRAE on the waste water treatment problems

Overall, social and environmental responsibility for researchers in the team involves using mathematical
expertise to address societal issues, promote inclusivity, and contribute to environmental sustainability
through research, collaboration, and outreach efforts.

6 Highlights of the year

• ANR Project NOCIME has been accepted

• Regional project STARS of Jin Gyu Lee has been accepted

• Almost all members of the team visited IEEE CDC in Singapore, where our team kept 1% of the total

number of accepted publications

• Among 28 journal publications of the team this year, 7 are in Automatica and 10 in IEEE TAC (the

top journals in the domain of the theory of control), which is 60% of scientific production

Project VALSE

7

7 New software, platforms, open data

7.1 New software

7.1.1 HCS Toolbox

Name: Homogeneous Systems Control Toolbox (HSC Toolbox) for MATLAB

Keywords: Control design, Matlab, Homogeneity

Functional Description: Homogeneous Systems Control Toolbox (HCS Toolbox) for MATLAB is a collec-
tion of functions for design and tuning of control systems with improved control quality (faster
convergences, better robustness, smaller overshoots, etc) based on the concept of a dilation sym-
metry (homogeneity). Homogeneous controllers/observers design well as procedures for upgrading
of existing linear controllers/observers to nonlinear (homogeneous) ones are developed for both
Single-Input Single-Output (SISO) and Multiply-Input Multiply-Output (MIMO) systems.

Release Contributions: HCS Toolbox for MATLAB ver. 0.1

This is the first release of HCS Toolbox for MATLAB. The list of MATLAB functions provided for
homogeneous control systems design: (Homogeneous Objects) hnorm - computation of homo-
geneous norm hproj - computation of homogeneous projection hcurve - generation of points of a
homogeneous curve hsphere - generation of a random grid on a homogeneous sphere (Homogen-
eous Control Design) hpc_design - Homogeneous Proportional Control (HPC) design hpci_design -
Homogeneous Proportional-Integral Control (HPIC) design hsmc_design - Homogeneous Sliding
Mode Controller (HSMC) design hsmci_design - design of HSMC with Integral action fhpc_design -
Fixed-time HPC design fhpic_design - Fixed-time HPIC design lpc2hpc - upgrading Linear Propor-
tional Control (LPC) to HPC lpic2hpc - upgrading Linear PI control (LPIC) to HPIC (Discretization of
Homogeneous Control) e_hpc - explicit discretization of HPC e_hpc - semi-implicit discretization
of HPC c_hpc - consistent discretization of HPC e_hpic - explicit discretization of HPIC e_hsmc -
explicit discretization of HSMC si_hsmc - semi-implicit explicit discretization of HSMC e_hsmci -
explicit discretization of HSMC with Integral action e_fhpc - explicit discretization of Fixed-time
HPC si_fhpc - semi-implicit discretization of Fixed-time HPC e_fhpic - explicit discretization of
Fixed-time HPIC (Homogeneous Observer Design) ho_design - Homogeneous Observer (HO)
design fho_design - Fixed-time HO design lo2ho - upgrading Linear Observer (LO) to HO (Discret-
ization of Homogeneous Observer) e_ho - explicit Euler discretization of HO e_fho - explicit Euler
discretization of FHO si_ho - semi-implicit discretization of HO si_fho - semi-implicit discretization
of FHO (Block forms ) block_con - transformation to block controlability form bloc_obs - trans-
formation to block bservability form trans_con - transformation to partial block controlability form
trans_con - transformation to partial block observability form output_form - transformation to
reduced order output control system (Examples) demo_hnorm - demo of computation of a homo-
geneous norm demo_hsphere - plot of homogeneous balls in 2D demo_hpc - demo of HPC design
and simulation demo_hpic - demo of HPIC design and simulation demo_hsmc - demo of HSMC
design and simulation demo_hsmci - demo of HSMCI design and simulation demo_fhpc - demo of
FHPC design and simulation demo_fhpic - demo of FHPIC design and simulation demo_lpc2hpc -
demo of upgrading LPC to HPC/FHPC demo_lpic2hpic - demo of upgrading LPIC to HPIC/FHPIC
demo_ho - demo of HO design and simulation demo_fho - demo of FHO design and simulation
demo_lo2ho - demo of upgrading LO to HO/FHO For more details please read the documentation:
HCS_doc.pdf

URL: https://gitlab.inria.fr/polyakov/hcs-toolbox-for-matlab

Author: Andrey Polyakov

Contact: Andrey Polyakov

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Inria Annual Report 2023

8 New results

8.1 Analysis and design of homogeneous and finite-time stable systems

Participants: Denis Efimov, Andrey Polyakov.

Input-to-state stability (ISS) is one of the most utilizable robust stability properties for nonlinear
dynamical systems, while (nearly) fixed-time convergence is a kind of decay for trajectories of disturbance-
free systems that is independent in initial conditions. The presence of both these features for a system can
be checked by existence of a proper Lyapunov function. The objective of [5] was to provide the conditions
for a converse result that (nearly) fixed-time input-to-state stable systems admit a respective Lyapunov
function. Similar auxiliary results for uniform finite-time stability and uniform (nearly) fixed-time stability
are obtained.

Usually, singularly perturbed models are used to justify the decomposition of the interconnected sys-
tems into the Main Dynamics (MD) and the Parasitic Dynamics (PD). In [15], the effect of a homogeneous
PD on the stability of a homogeneous MD, when homogeneity degrees are possibly different, is studied
via ISS approach in the framework of singular perturbations. Proposed analysis discovers three kinds of
stability in the behavior of such an interconnection by assuming that both, regulated MD and unforced
PD, are globally asymptotically stable.

The paper [28] develops control algorithms for a class of affine nonlinear systems using the so-
called canonical homogeneous representation. It is demonstrated that such a representation exists for
any homogeneous vector field bounded on the unit sphere. It is shown that canonical homogeneous
representation is useful for LMI-based control design and stability analysis of nonlinear systems.

Non-overshooting stabilization is a form of safe control where the setpoint chosen by the user is at the
boundary of the safe set. Exponential non-overshooting stabilization, including suitable extensions to
systems with deterministic and stochastic disturbances, has been solved previously. In [20], we develop
homogeneous feedback laws for fixed-time nonovershooting stabilization of nonlinear systems that are
input-output linearizable with a full relative degree, i.e., for systems that are diffeomorphically equivalent
to the chain of integrators. These homogeneous feedback laws can also assume the secondary role of
’fixed-time safety filters’ (FxTSf filters) which keep the system within the closed safe set for all time but, in
the case where the user’s nominal control commands approach to the unsafe set, allow the system to
reach the boundary of the safe set no later than a desired time that is independent of nominal control
and independent of the value of the state at the time the nominal control begins to be overridden.

The problem of finite-time stabilization of a linear plant with an optimization of both a settling time
and an averaged/weighted control energy is studied using the concept of generalized homogeneity in
[19]. It is shown that the optimal finite-time stabilizing control in this case can be designed by means of
solving a simple linear algebraic equation. Robustness of the obtained control law is studied.

The paper [6] addresses the problem of input-to-state stabilization for heat equation with external
input via boundary control strategy. Following our previous results, based on the backstepping approach,
a switching boundary control law depending on the system state is designed. By estimating the upper
bound of kernel functions, switching levels are determined and commutation law is further constructed.
For the chosen switched control, the well-posedness property is verified. It is proved that the resulting
system is ISS, and the solutions of the system will not exceed the highest admissible level dependent on
the disturbance amplitude. Meanwhile, a stronger result is also obtained, that is the finite-time stability
for the disturbance-free system.

8.2 Analysis and design for time-delay systems

Participants: Denis Efimov.

For a class of nonlinear systems with homogeneous right-hand sides of non-zero degree and distrib-
uted delays, the problem of stability robustness of the zero solution with respect to time-varying perturb-

Project VALSE

9

ations multiplied by a nonlinear functional gain is studied in [2]. It is assumed that the disturbance-free
and delay-free system (that results after substitution of non-delayed state for the delayed one) is globally
asymptotically stable. First, it is demonstrated that in the disturbance-free case the zero solution is either
locally asymptotically stable or practically globally asymptotically stable, depending on the homogeneity
degree of the delay-free counterpart. Second, using averaging tools several variants of the time-varying
perturbations are considered and the respective conditions are derived evaluating the stability margins
in the system. The results are obtained by a careful choice and comparison of Lyapunov-Krasovskii
and Lyapunov-Razumikhin approaches. Finally, the obtained theoretical findings are illustrated on two
mechanical systems.

For input-affine nonlinear dynamical systems, an ISS analysis with respect to (weighted) average
values of exogenous perturbations is proposed in [4]. The time-delay method is used to represent the
system in a suitable form for investigation: a kind of neutral-type differential equation. The introduced
approach allows the asymptotic gains with respect to zero-mean periodic signals to be evaluated for
nonlinear systems (an analogue of Bode magnitude plot), as well as for integral ISS (iISS) systems with
periodic inputs. The results are illustrated on the class of homogeneous systems.

8.3 Discretisation of homogeneous systems

Participants: Denis Efimov, Andrey Polyakov.

The paper [18] proposes a discretization (sampled-time implementation) algorithm for a class of
homogeneous controllers for linear time-invariant systems preserving the finite-time and nearly fixed-
time stability properties. The sampling period is assumed to be constant. Both single-input and multiple-
input cases are considered. The robustness (ISS) of the obtained sampled-time control system is studied
as well.

The paper [16] is dedicated to the experimental analysis of discrete-time differentiators implemented
in closed-loop control systems. To this end, two laboratory setups, namely an electro-pneumatic system
and a rotary inverted pendulum have been used to implement 25 different differentiators. Since the
selected laboratory setups behave differently in the case of dynamic response and noise characteristics, it
is expected that the results remain valid for a wide range of control applications. The validity of several
theoretical results, which have been already reported in the literature using mathematical analysis and
numerical simulations, has been investigated, and several comments are provided to allow one to select
an appropriate differentiation scheme in practical closed-loop control systems.

8.4 Homogenization through controls

Participants:

Andrey Polyakov.

In [13], the leader-following consensus problem for multi-agent systems is considered. Each agent is
assumed to be modeled by a linear multi-input system. A novel (generalized homogeneous) consensus
control protocol is designed under the assumption that there are some uncertainties in the dynamic of
the leader. Some LMIs are derived to select the control parameters in order to ensure the ISS and global
finite-time stability of the consensus errors with desired homogeneity degrees.

The methodology of the unit sliding mode control design (known since 1970s) for linear systems is
revised based on the concept of the generalized homogeneity in [17]. The restriction about a consistency
of the number of control inputs with the dimension of the sliding surface is eliminated. A simple
procedure of control tuning based on a known maximal magnitude of matched perturbations is developed.
To deal with perturbations of unknown magnitude, a homogeneous sliding mode control with integral
action is designed as well.

A generalized homogeneous control with integral action for a multiple-input plant operating under
uncertainty conditions is designed in [26]. The stability analysis is essentially based on a special version

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Inria Annual Report 2023

of the non-smooth Lyapunov function theorem for differential equations with discontinuous right-hand
sides. A Lyapunov function for analysis of the closed-loop system is presented. For negative homogeneity
degree, this Lyapunov function becomes a strict Lyapunov function allowing an advanced analysis to be
provided. In particular, the maximum control magnitude and the settling-time of the closed-loop system
are estimated and a class of disturbances to be rejected by the control law is characterized. The control
parameters are tuned by solving a system of LMIs, whose feasibility is proved at least for small (close to
zero) homogeneity degrees.

8.5 Control and estimation for Persidskii systems

Participants: Denis Efimov, Rosane Ushirobira.

Generalized Persidskii systems (or Lur’e systems) represent the dynamics described by the superposi-
tion of a linear part with multiple sector nonlinearities and exogenous perturbations. They can be used
to model many physical and engineering phenomena.

The paper [14] studies the trajectory behavior evaluation for generalized Persidskii systems with an
essentially bounded input on a finite time interval. Also, the notions of annular settling and output
annular settling for general nonlinear systems are introduced, and the respective stability conditions are
porposed. These conditions are based on the verification of linear matrix inequalities. An application to
recurrent neural networks illustrates the usefulness of the proposed notions and conditions.

The paper [7] considers the state estimation problem for a class of non-autonomous nonlinear sys-
tems. We propose conditions on the existence and stability of a nonlinear observer based on the invariant
manifold approach in both continuous and discrete-time scenarios. The requirements are formulated us-
ing linear matrix equalities and LMIs. We present two possible applications of the result: a reduced-order
observer (e.g., an observer for unmeasured states) and regression in linear and nonlinear, continuous-and
discretetime settings. With nonlinear regression being a sophisticated case, the parameter estimation
problem for a particular output equation (when the fusion of linear and nonlinear sensors is weighted) is
investigated.

The article [22] deals with the problem of time-varying parameter identification in dynamical regres-
sion models affected by disturbances. The disturbances comprise time-dependent external perturbations
and nonlinear unmodeled dynamics. With this aim in mind, we propose a robust nonlinear adaptive
observer. The algorithm ensures the asymptotic convergence of the parameter identification error to an
acceptably small region around the origin in the presence of disturbances. The synthesis of the adaptive
observer is given in terms of linear matrix inequalities since the error dynamics is reduced to Persidskii
form, providing a constructive design method.

8.6 Control of robotic systems

Participants:

Andrey Polyakov.

The paper [27] deals with the tracking problem for the unicycle mobile robot with slippage effects. A
homogeneous controller is developed based on a particular cascade control strategy. The robustness
of the closed-loop system is studied. The design is essentially based on the canonical homogeneous
norm being a Lyapunov function of the system. The (finite-time or exponential) convergence rate of the
homogeneous controller can be tuned by a proper selection of the so-called homogeneity degree. Some
experimental results illustrate the performance of the proposed homogeneous control in the UMR QBot2
by Quanser.

The paper [23] contributes to the design of a second order sliding-mode controller for the trajectory
tracking problem in perturbed unicycle mobile robots. The proposed strategy takes into account the
design of two particular sliding variables, which ensure the convergence of the tracking error to the
origin in a finite time despite the effect of some external perturbations. The straightforward structure

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of the controller is simple to tune and implement. The global, uniform and finite-time stability of the
closed-loop tracking error dynamics is demonstrated by means of Lyapunov functions. Furthermore, the
performance of the proposed approach is validated through some experiments using a QBot2 unicycle
mobile robot.

8.7 Estimation under communication constraints

Participants: Denis Efimov.

In the paper [25], an approach is proposed for the remote observation of a dynamical system through a
data-rate constrained communication channel. The focus is put on discrete-time systems with a Lipschitz
nonlinearity, driven by an external signal, and subject to bounded state perturbation and measurement
error. The problem at hand is providing estimates of system’s state at a remote location, which is
connected via a channel, which can only sent limited numbers of bits per unit of time. A solution, named
observation scheme, is proposed in the form of several interacting agents. This solution is designed such
that the maximum observation error is upper-bounded by a computable quantity dependent on system
constants and selectable parameters. The scheme is designed in an event-triggered fashion, such that the
actual communication rate is sometimes much lower than the theoretically evaluated maximum one.

8.8 Synchronization and multistability

Participants: Denis Efimov, Rosane Ushirobira, Jin Gyu Lee.

We present new results for global boundedness of state periodic systems in [24]. Thereby, we address
both the case of systems, whose dynamics is periodic with respect to a part of the state vector and the
case of systems, whose dynamics is periodic with respect to all state variables. Both classes of systems are
of high relevance in diverse and timely applications. To derive the results the notion of strong Leonov
functions is refined. The main results are complemented by a number of relaxations based on the concpet
of weak Leonov functions.

In the paper [3], we study the problem of robust stabilization of affine nonlinear multistable systems
in the presence of exogenous disturbances. The results are based on the theory of ISS and iISS for
systems with multiple invariant sets. The notions of ISS and iISS control Lyapunov functions (CLFs) and
the small control property are extended within the multistability framework. Such properties are also
complemented by the concept of a weak iISS CLF and corresponding small control property. It is verified
that the universal control formula can be applied to yield the ISS (iISS) property for the closed-loop
system. The efficiency of the extended CLF framework in the multistable sense is illustrated for a Duffing
system and in application to a noise-induced transition in a semiconductor-gas-discharge gap system.
When a group of heterogeneous node dynamics are diffusively coupled with a high coupling gain,
the group exhibits a collective emergent behavior which is governed by a simple algebraic average of
the node dynamics called the blended ones. This finding has been utilized for designing heterogeneous
multi-agent systems by building the desired blended dynamics first and then splitting it into the node
dynamics. However, to compute the magnitude of the coupling gain, each agent needs to know global
information such as the number of participating nodes, the graph structure, and so on, which prevents a
fully decentralized design of the node dynamics in conjunction with the coupling laws. To resolve this
issue, the idea of funnel control, which is a method for adaptive gain selection, was exploited in [11].

A discrete-time version of the blended dynamics theorem is proposed in [8] that can be used for design
of distributed computation algorithms. The blended dynamics theorem enables to predict the behavior
of heterogeneous multi-agent systems. Therefore, once we get a blended dynamics for a particular
computational task, design idea of node dynamics for individual heterogeneous agents can easily occur.
In the continuous-time case, prediction by blended dynamics was enabled by high coupling gain among
neighboring agents. In the discrete-time case, we propose an equivalent action.

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Inria Annual Report 2023

The paper [12] examines how weak synaptic coupling can achieve rapid synchronization in hetero-
geneous networks. The assumptions aim at capturing the key mathematical properties that make this
possible for biophysical networks. In particular, the combination of nodal excitability and synaptic
coupling are shown to be essential to the phenomenon.

The paper [10] investigates the finite-time stability and nearly fixed-time stability of nonlinear im-
pulsive systems with destabilizing impulses. A Lyapunov inequality with linear terms has been used to
derive sufficient conditions based on the dwell time (DT) and average dwell time (ADT) properties of
impulsive sequences to ensure stability of the system. The main results of this paper are applied to the
synchronization problem of impulsive neural networks with destablizing impulses.

9 Bilateral contracts and grants with industry

9.1 Bilateral contracts with industry

Participants: Denis Efimov, Rosane Ushirobira.

• 52 Hertz is a startup (Brest, France) that develops an underwater communication device for divers.
The goal of this contract was to develop an intelligent filtering algorithm that compensates for the
voice deformation during underwater vocal communication through the device. The code for the
filter was written in Matlab, with further help for its adaptation in Python and C.

10 Partnerships and cooperations

10.1 International initiatives

10.1.1 Participation in other International Programs

ECOS-Nord, Mexico

Participants: Denis Efimov, Andrey Polyakov, Rosane Ushirobira.

Title: Artificial Intelligence-based Control Approaches for Multiple Mobile Robots

Partner Institution(s):

• IT Laguna, Mexico

• Instituto Politécnico Nacional, Mexico

Date/Duration: 2021–2023

Additionnal info/keywords: This project was focused on studying several tracking tasks for autonomous
mobile robot systems, particularly unmanned aerial vehicles and wheeled mobile robots. This
project aimed to develop robust control and navigation schemes by combining the methods of
artificial intelligence and control theory.

PHC Aurora

Participants: Denis Efimov, Andrey Polyakov, Rosane Ushirobira, Jin Gyu Lee.

Title: Equivalent nonlinear control methods for digitalization in robotics and autonomous systems

Partner Institution(s):

• University of Agder, Norway

Project VALSE

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Date/Duration: 2023-2024

Additionnal info/keywords: The robotic and autonomous systems rely heavily on the complex, often
distributed, and hierarchical control systems, which ensure main functionalities with a flexible and
safe operation. The classical automatic controllers with feedback from the acquisition and percep-
tion devices continue to experience the new challenges coming from an increasing complexity in
the dynamic behavior of the systems to be controlled on the one hand, and from the digitalization
and associated transformations of data, their spatial availability and communication time delays
on the other hand. To propose the advanced nonlinear control methods which, however, would be
equivalent (in terms of simplicity of tuning and implementation) to the widely accepted standard
linear controls (such as PID), and in this way would be more accessible for future applications, is
the scientific scope of this project.

10.2 International research visitors

10.2.1 Visits of international scientists

Inria International Chair

Participants: Denis Efimov, Andrey Polyakov, Rosane Ushirobira, Jin Gyu Lee.

Leonid Fridman, UNAM, until Jan 2023

Other international visits to the team

Ariana Gutierrez

Status: PhD

Institution of origin: IT Laguna

Country: Mexico

Dates: from Aug 2023 until Oct 2023

Context of the visit: ECOS Nord

Mobility program/type of mobility: research stay

Jose Antonio Ortega

Status: PhD

Institution of origin: UNAM

Country: Mexico

Dates: from May 2023 until Jun 2023

Context of the visit: Consyt grant

Mobility program/type of mobility: research stay

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Inria Annual Report 2023

Hector Rios Barajas

Status: researcher

Institution of origin: IT Laguna

Country: Mexico

Dates: from Aug 2023 until Sep 2023

Context of the visit: ECOS Nord

Mobility program/type of mobility: research stay

Manuel Mera

Status: researcher

Institution of origin: Instituto Politécnico Nacional

Country: Mexico

Dates: from Aug 2023 until Sep 2023

Context of the visit: Inria invited professor

Mobility program/type of mobility: research stay

Ankit Kumar

Status: PhD

Institution of origin: IIT Delhi

Country: India

Dates: from Mar 2023 until May 2023

Context of the visit: CEFIPRA mobility grant

Mobility program/type of mobility: research stay

10.3 National initiatives

10.3.1 ANR

• NOCIME (New Observation and Control Issues Motivated by Epidemiology), coordinator Pierre-

Alexandre Bliman (Inria, Paris)

• SyNPiD (Synchronization in power networks with periodic dynamics), coordinators Denis Efimov
(Inria, France) and J. Schiffer (Brandenburg University of Technology Cottbus-Senftenberg, Ger-
many)

10.4 Regional initiatives

• Project STARS "Practical design for interconnected CPSs by synchronization enforcement" of Jin

Gyu Lee

11 Dissemination

The members of the team serve as reviewers for major journals and conferences in the field of the theory
of control and automation.

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11.1 Promoting scientific activities

11.1.1 Scientific events: organisation

Member of the conference program committees

• Denis Efimov, IFAC World Congress, Yokohama, Japan

11.1.2 Journal

Member of the editorial boards

• Denis Efimov, Associate editor, IFAC Journal on Nonlinear Analysis: Hybrid Systems

• Denis Efimov, Associate editor, IEEE Transactions on Automatic Control

• Denis Efimov, Associate editor, Automatica

• Rosane Ushirobira, Associate editor, Asian Journal of Control

• Rosane Ushirobira, Associate editor, Trends in Computational and Applied Mathematics (TEMA)

11.1.3 Invited talks

• Denis Efimov, Hangzhou Dianzi University, China

• Denis Efimov, Xidian University, Xi’an, China

• Andrey Polyakov, Xidian University, Xi’an, China

11.1.4 Leadership within the scientific community

• Denis Efimov, Senior member IEEE

• Denis Efimov, Member of IFAC TC 1.2. Adaptive and Learning Systems

• Denis Efimov, Publication vice-chair of IFAC TC 9.2. Systems and Control for Societal Impact

• Denis Efimov, Executive committee member, IEEE CSS Technical Committee on Variable Structure

and Sliding Mode Control

• Denis Efimov, Co-chair of European PhD Award on Control for Complex and Heterogeneous

Systems

• Rosane Ushirobira, Scientific Officer at CIMPA (Centre International de Mathématiques Pures et

Appliquées)

11.1.5 Research administration

• Rosane Ushirobira, Elected member of the CE Inria

• Rosane Ushirobira, President of the CER (Commission des emplois de recherche) Inria Lille

• Andrey Polyakov, Jury member of the CRCN/ISFP Inria Lille

• Rosane Ushirobira, Jury member of the CRCN/ISFP Inria Lyon; CoS MCF CNU 61 IUT Lille

11.2 Teaching - Supervision - Juries

11.2.1 Teaching

• Licence: Rosane Ushirobira, Basic courses in Linear algebra and Calculus, 71h, L3, Polytech Lille

• Master: Jin Gyu Lee, Dynamical systems, 17h, M2, Université de Lille

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11.2.2 Juries

Inria Annual Report 2023

The members of the team participated in numerous juries for Ph.D. defense.

11.3 Popularization

11.3.1 Internal or external Inria responsibilities

• Denis Efimov, Member of IES comittee

• Rosane Ushirobira, Scientific Officer for Scientific Popularization

• Rosane Ushirobira, Organizer of 30 min. of science (monthly seminar for scientists in the center)

11.3.2 Interventions

• Rosane Ushirobira, Organizer of CHICHE sessions in Lille Academy, gave 13 talks to high-school

students within this framework

• Rosane Ushirobira, Organizer of the 3rd Rendez-vous des Jeunes Mathématiciennes et Inform-

aticiennes (RJMI) Inria Lille

12 Scientific production

12.1 Publications of the year

International journals

[1] A. Aleksandrov, D. Efimov and E. Fridman. ‘On local ISS of nonlinear second-order time-delay
systems without damping †’. In: International Journal of Robust and Nonlinear Control (2024). URL:
https://inria.hal.science/hal-04396969.

[2] A. Aleksandrov, D. Efimov and E. Fridman. ‘Stability of homogeneous systems with distributed
delay and time-varying perturbations’. In: Automatica 153 (July 2023), p. 111058. DOI: 10.1016/j
.automatica.2023.111058. URL: https://inria.hal.science/hal-03777752.

[3] N. F. Barroso, R. Ushirobira and D. Efimov. ‘Control Lyapunov function method for robust stabiliz-
ation of multistable affine nonlinear systems’. In: International Journal of Robust and Nonlinear
Control (Mar. 2023). URL: https://inria.hal.science/hal-04042760.

[4] D. Efimov and E. Fridman. ‘On ISS with respect to average value of disturbances: a time-delay
approach’. In: IEEE Transactions on Automatic Control (2023). URL: https://inria.hal.scienc
e/hal-04309870.

[5] D. Efimov and A. Polyakov. ‘On converse Lyapunov theorem for fixed-time input-to-state stability’.
In: SIAM Journal on Control and Optimization (2023). URL: https://inria.hal.science/hal-
04274297.

[6] X.-X. Han, D. Efimov, A. Polyakov and K.-N. Wu. ‘Input-to-state stability analysis of heat equation
with boundary finite-time control’. In: Automatica (2023). URL: https://inria.hal.science/h
al-04268174.

[7] A. Khalin, D. Efimov and R. Ushirobira. ‘On robust observer design for a class of time-varying
continuous-and discrete-time Persidskii systems’. In: IEEE Transactions on Automatic Control
(2023). URL: https://inria.hal.science/hal-04283035.

[8]

J. W. Kim, J. G. Lee, D. Lee and H. Shim. ‘A Design Method of Distributed Algorithms via Discrete-
time Blended Dynamics Theorem’. In: Automatica (2023). URL: https://hal.science/hal-042
35062.

[9] M. Korotina, S. Aranovskiy, R. Ushirobira, D. Efimov and J. Wang. ‘A note on fixed-and discrete-time
estimation via the DREM method’. In: IEEE Transactions on Automatic Control (Jan. 2023). URL:
https://inria.hal.science/hal-04393160.

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[10] R. Kumar and D. Efimov. ‘Finite/nearly Fixed-Time stability of Nonlinear Impulsive Systems with
Destabilizing Impulses and its Application to Neural Networks’. In: Communications in Nonlinear
Science and Numerical Simulations (2023). URL: https://inria.hal.science/hal-04125430.

[11]

J. G. Lee, T. Berger, S. Trenn and H. Shim. ‘Edge-wise funnel output synchronization of heterogen-
eous agents with relative degree one’. In: Automatica 156 (Oct. 2023), p. 111204. DOI: 10.1016/j.a
utomatica.2023.111204. URL: https://hal.science/hal-04235016.

[12]

J. G. Lee and R. Sepulchre. ‘Rapid and robust synchronization via weak synaptic coupling’. In:
Automatica (2023). URL: https://hal.science/hal-04235088.

[13] M. Li, A. Polyakov and G. Zheng. ‘On Generalized Homogeneous Leader-following Consensus
Control for Multi-agent Systems’. In: IEEE Transactions on Control of Network Systems (2024). DOI:
10.1109/TCNS.2023.3290429. URL: https://hal.science/hal-04390600.

[14] W. Mei, D. Efimov and R. Ushirobira. ‘On annular short-time stability conditions for generalized
Persidskii systems’. In: International Journal of Control (Sept. 2023). URL: https://inria.hal.s
cience/hal-04189087.

[15]

J. Mendoza-Avila, D. Efimov, L. Fridman and J. A. Moreno. ‘On Stability of Homogeneous Systems
in Presence of Parasitic Dynamics’. In: IEEE Transactions on Automatic Control 11 (1st Nov. 2023).
URL: https://inria.hal.science/hal-03562148.

[16] M. R. Mojallizadeh, B. Brogliato, A. Polyakov, S. Selvarajan, L. Michel, F. Plestan, M. Ghanes, J.-P.
Barbot and Y. Aoustin. ‘Discrete-time differentiators in closed-loop control systems: experiments
on electro-pneumatic system and rotary inverted pendulum’. In: Control Engineering Practice 136
(2023), pp. 1–28. DOI: 10.1016/j.conengprac.2023.105546. URL: https://inria.hal.scien
ce/hal-03125960.

[17] A. Polyakov. ‘Homogeneous Unit Sliding Mode Control’. In: IEEE Transactions on Automatic Control
(16th May 2023). DOI: 10.1109/TAC.2023.3276893. URL: https://inria.hal.science/hal-
03868972.

[18] A. Polyakov, D. Efimov and X. Ping. ‘Consistent discretization of homogeneous finite/fixed-time
controllers for LTI systems’. In: Automatica 155 (1st Sept. 2023), p. 111118. URL: https://hal.sci
ence/hal-04071575.

[19] A. Polyakov, D. Efimov and X. Ping. ‘Energetically optimal finite-time stabilization of generalized
homogeneous linear systems’. In: IEEE Transactions on Automatic Control (2023). URL: https://i
nria.hal.science/hal-03993740.

[20] A. Polyakov and M. Krstic. ‘Finite-and Fixed-Time Nonovershooting Stabilizers and Safety Filters by
Homogeneous Feedback’. In: IEEE Transactions on Automatic Control (16th Jan. 2023), pp. 1–16.
DOI: 10.1109/TAC.2023.3237482. URL: https://inria.hal.science/hal-03544744.

[21] A. Polyakov and M. Krstic. ‘Fixed-time Stabilization with a Prescribed Constant Settling Time by
Static Feedback for Delay-Free and Input Delay Systems’. In: International Journal of Robust and
Nonlinear Control (2024). URL: https://hal.science/hal-04390695.

[22] H. Ríos, A. Ferreira de Loza, D. Efimov and R. Franco. ‘An LMI-based Robust Nonlinear Adaptive
Observer for Disturbed Regression Models’. In: IEEE Transactions on Automatic Control (2023).
URL: https://inria.hal.science/hal-04333541.

[23] H. Ríos, M. Mera and A. Polyakov. ‘Perturbed Unicycle Mobile Robots: A Second-Order Sliding-
Mode Trajectory Tracking Control’. In: IEEE Transactions on Industrial Electronics (1st May 2023),
pp. 1–9. DOI: 10.1109/TIE.2023.3270520. URL: https://hal.science/hal-04072004.

[24]

J. Schiffer and D. Efimov. ‘Strong and weak Leonov functions for global boundedness of state
periodic systems’. In: IEEE Transactions on Automatic Control (2023). URL: https://inria.hal
.science/hal-03779687.

[25] Q. Voortman, D. Efimov, A. Pogromsky, J.-P. Richard and H. Nijmeijer. ‘Remote State Estimation of
Steered Systems with Limited Communications: an Event-Triggered Approach’. In: IEEE Transac-
tions on Automatic Control (2023). URL: https://inria.hal.science/hal-04201562.

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Inria Annual Report 2023

[26] Y. Zhou, A. Polyakov and G. Zheng. ‘Generalized homogeneous control with integral action’. In:
International Journal of Robust and Nonlinear Control (25th Jan. 2023). DOI: 10.1002/rnc.6612.
URL: https://inria.hal.science/hal-03993724.

[27] Y. Zhou, H. Ríos, M. Mera, A. Polyakov, G. Zheng and A. Dzul. ‘Homogeneity-Based Control Strategy
for Trajectory Tracking in Perturbed Unicycle Mobile Robots’. In: IEEE Transactions on Control
Systems Technology 32.1 (2024), pp. 274–281. DOI: 10.1109/TCST.2023.3300273. URL: https:
//hal.science/hal-04390587.

[28] K. Zimenko, A. Polyakov and D. Efimov. ‘Homogeneous Systems Stabilization Based on Convex
Embedding ⋆’. In: Automatica 154 (1st Aug. 2023), p. 111108. URL: https://inria.hal.science
/hal-04037564.

International peer-reviewed conferences

[29] A. Aleksandrov, D. Efimov and E. Fridman. ‘Analysis of homogeneous systems with distributed
delay using averaging approach’. In: IFAC 2023 - 22nd IFAC World Congress. Yokohama, Japan,
9th July 2023. URL: https://inria.hal.science/hal-04176143.

[30] A. Aleksandrov, D. Efimov and E. Fridman. ‘On stability of second-order nonlinear time-delay sys-
tems without damping’. In: CDC 2023 - 62nd IEEE Conference on Decision and Control. Singapore,
Singapore, 13th Dec. 2023. URL: https://inria.hal.science/hal-04390334.

[31] S. Aranovskiy, R. Ushirobira and D. Efimov. ‘On DREM regularization and unexcited linear re-
gression estimation’. In: 62nd IEEE Conference on Decision and Control. SINGAPORE, Singapore,
13th Dec. 2023. URL: https://centralesupelec.hal.science/hal-04073212.

[32] G. Dadjo, D. Efimov, J. Harmand, A. Rapaport and R. Ushirobira. ‘An adaptive observer for time-
varying nonlinear systems - application to a crop irrigation model’. In: 62nd IEEE Conference on
Decision and Control. Singapore, Singapore, 13th Dec. 2023. URL: https://hal.inrae.fr/hal-
04174481.

[33] D. Efimov and I. Kolmanovsky. ‘Homogeneity with respect to a part of variables and accelerated
stabilization’. In: CDC 2023 - 62nd IEEE Conference on Decision and Control. Singapore, Singapore,
13th Dec. 2023. URL: https://inria.hal.science/hal-04390318.

[34] D. Efimov, A. Polyakov, K. Zimenko and J. Wang. ‘On hyperexponential stabilization of double
integrator in continuous and discrete time’. In: IFAC 2023 - 22nd IFAC World Congress. Yokohama,
Japan, 9th July 2023. URL: https://inria.hal.science/hal-04176126.

[35] M. Fang, P.-A. Bliman, D. Efimov and R. Ushirobira. ‘Nonlinear Adaptive Observers for an SIS System
Counting Primo-infections’. In: 22nd World Congress of the International Federation of Automatic
Control. Yokohama, Japan, 9th July 2023. URL: https://inria.hal.science/hal-04063936.

[36] A. Gutiérrez, H. Rios, M. Mera, D. Efimov and R. Ushirobira. ‘An Interval Predictor-based Robust
Control for a Class of Constrained Nonlinear Systems’. In: 62nd IEEE Conference on Decision and
Control. SINGAPORE, Singapore, Dec. 2023. URL: https://inria.hal.science/hal-04264554.

[37] S. V. Gutiérrez-Martínez, H. Ríos, M. Mera, T. Raïssi and D. Efimov. ‘A Robust Interval MPC for
Uncertain LPV Systems via Integral Sliding-Mode Control’. In: CDC 2023 - 62nd IEEE Conference
on Decision and Control. Singapore, Singapore, 13th Dec. 2023. URL: https://inria.hal.scien
ce/hal-04390287.

[38] A. Khalin, D. Efimov and R. Ushirobira. ‘On observer design for a class of Persidskii systems based
on steady-state estimation’. In: IFAC 2023 - 22nd IFAC World Congress. Yokohama, Japan, 9th July
2023. URL: https://inria.hal.science/hal-04176170.

[39] M. Korotina, S. Aranovskiy, R. Ushirobira, D. Efimov and J. Wang. ‘Fixed-time parameter estimation
via the discrete-time DREM method’. In: IFAC-PapersOnLine. 22nd IFAC World Congress. Vol. 56.
2. YOKOHAMA, Japan, July 2023, pp. 4013–4018. DOI: 10.1016/j.ifacol.2023.10.1382. URL:
https://hal.science/hal-04390727.

[40]

J. G. Lee and A. Astolfi. ‘Realization from moments: The linear case’. In: IEEE Conference on
Decision and Control. Singapore, Singapore, 13th Dec. 2023. URL: https://hal.science/hal-0
4235115.

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[41] M. Li, A. Polyakov, G. Zheng and X. Ping. ‘On Prescribed-time Cooperative State Estimation of LTI
Plants’. In: IFAC 2023 - 22nd World Congress of the International Federation of Automatic Control.
Yokohama, Japan, 9th July 2023. URL: https://hal.science/hal-04059864.

[42] G. Magnani, A. dos Reis de Souza, M. Cassaro, J.-M. Biannic, H. Evain and L. Burlion. ‘Command
governor-based adaptive control for constrained linear systems in presence of unmodelled dynam-
ics’. In: ACC 2023 - American Control Conference. San Diego, United States: IEEE, 31st May 2023,
pp. 2387–2392. DOI: 10.23919/ACC55779.2023.10156442. URL: https://hal.science/hal-0
4220211.

[43]

[44]

[45]

[46]

J. Mendoza-Avila, D. Efimov, J. Á. Mercado Uribe and J. Schiffer. ‘Design of Controls for Bounded-
ness of Trajectories of Multistable State Periodic Systems’. In: Proc. 62th IEEE Conference on
Decision and Control (CDC). Singapore, Singapore, 12th Dec. 2023. URL: https://inria.hal.sc
ience/hal-04298554.

J. Mendoza-Avila, J. Á. Mercado Uribe, D. Efimov and J. Schiffer. ‘Design of controls for ISS and
Integral ISS Stabilization of Multistable State Periodic’. In: IFAC 2023 - The 22nd World Congress of
the International Federation of Automatic Control. Yokohama, Japan, 9th July 2023. URL: https:
//inria.hal.science/hal-04176442.

J. Á. Mercado Uribe, J. Mendoza-Avila, D. Efimov and J. Schiffer. ‘A Control Leonov Function
Guaranteeing Global ISS of Two Coupled Synchronverters’. In: Proc. 62th IEEE Conference on
Decision and Control (CDC). Singapore, France, 12th Dec. 2023. URL: https://inria.hal.scie
nce/hal-04298525.

J. Á. Mercado Uribe, J. Mendoza-Avila, D. Efimov and J. Schiffer. ‘A Leonov Function for Almost
Global Synchronization Conditions in Acyclic Networks of Heterogeneous Kuramoto Oscillators’.
In: IFAC 2023 - 22nd IFAC World Congress. Yokohama, Japan, 9th July 2023. URL: https://inria
.hal.science/hal-04176145.

[47] A. Polyakov. ‘Generalized Homogeneous Unit Control’. In: IFAC 2023 - 22nd World Congress of the
International Federation of Automatic Control. Yokohama, Japan, 9th July 2023. URL: https://ha
l.science/hal-04059845.

[48] H. Ríos, M. Mera, T. Raïssi and D. Efimov. ‘An Integral Sliding-Mode-based Robust Interval Pre-
dictive Control for Perturbed Unicycle Mobile Robots’. In: CDC 2023 - 62nd IEEE Conference on
Decision and Control. Singapore, Singapore, 13th Dec. 2023. URL: https://inria.hal.science
/hal-04390300.

[49] H. Ríos, M. Mera and A. Polyakov. ‘A New Finite-Time Sliding-Mode Controller for a Class of Second-
Order Non-Linear Systems’. In: IFAC 2023 - 22nd World Congress of the International Federation of
Automatic Control. Yokohama, Japan, 9th July 2023. URL: https://hal.science/hal-04059833.

[50] R. Ushirobira and D. Efimov. ‘Constructing annihilators for parameter estimation in nonlinearly
parameterized signals’. In: IFAC 2023 - 22nd IFAC World Congress. Yokohama, Japan, 9th July 2023.
URL: https://inria.hal.science/hal-04176149.

[51] Y. Zhou, H. Ríos, M. Mera, A. Polyakov, G. Zheng and A. Dzul. ‘Trajectory Tracking in Unicycle
Mobile Robots: A Homogeneity-based Control Approach’. In: IFAC 2023 - 22nd World Congress of
the International Federation of Automatic Control. Yokohama, Japan, 9th July 2023. URL: https:
//hal.science/hal-04059857.

[52] K. Zimenko, D. Efimov and A. Polyakov. ‘Stability analysis and stabilization of systems with hyper-
exponential rates’. In: IFAC 2023 - 22nd IFAC World Congress. Yokohama, Japan, 9th July 2023. URL:
https://inria.hal.science/hal-04176160.

[53] K. Zimenko, D. Efimov, A. Polyakov and A. Kremlev. ‘On finite-time observers for linear systems’.
In: IFAC 2023 - 22nd IFAC World Congress. Yokohama, Japan, 9th July 2023. URL: https://inria
.hal.science/hal-04176154.

[54] K. Zimenko, D. Efimov, A. Polyakov and X. Ping. ‘Finite-time control protocol for uniform allocation
of second-order agents’. In: CDC 2023 - 62nd IEEE Conference on Decision and Control. Singapore,
Singapore, 13th Dec. 2023. URL: https://inria.hal.science/hal-04390264.

20

Inria Annual Report 2023

Scientific book chapters

[55] T. Sanchez, A. Polyakov and D. Efimov. ‘Lyapunov-based Consistent Discretization of Quasi-
Continuous High Order Sliding Modes’. In: Sliding-Mode Control and Variable-Structure Systems.
Vol. 490. Studies in Systems, Decision and Control. Springer International Publishing, 1st Nov. 2023,
pp. 205–228. DOI: 10.1007/978-3-031-37089-2_9. URL: https://hal.science/hal-043909
49.

Reports & preprints

[56] M. Ayamou, A. Polyakov and N. Espitia. Locally Homogeneous Finite-time Stabilization of Quasi-

Linear Systems. 23rd June 2023. URL: https://inria.hal.science/hal-04139119.

[57] M. Dadjo, A. Rapaport, J. Harmand, R. Ushirobira and D. Efimov. Water-minimizing strategies under
viability constraint for a crop fertirrigation model. 27th Oct. 2023. URL: https://hal.inrae.fr/h
al-04267286.

[58] D. Efimov, A. Polyakov and X. Ping. Interval Observation and Control for Continuous-Time Persidskii

Systems. 26th Sept. 2023. URL: https://inria.hal.science/hal-04217784.

[59] A. Polyakov. Homogeneous Artificial Neural Network. 29th Nov. 2023. URL: https://inria.hal.s

cience/hal-04313941.

[60] H. Tyagi and D. Efimov. Learning linear dynamical systems under convex constraints. 2nd Aug. 2023.

URL: https://hal.science/hal-04394297.

[61]

J. Zhang, C. Combastel, D. Efimov and A. Zolghadri. Robust Stability Analysis for Continuous-Time
Parameter-Varying Persidskii Systems. 4th Oct. 2023. URL: https://inria.hal.science/hal-0
4228192.

[62] K. Zimenko, D. Efimov and A. Polyakov. Homogeneous Systems Stabilization Based on Convex

Embedding. Inria, 2023. URL: https://inria.hal.science/hal-04037561.

12.2 Cited publications

[63] H. Ahmed, R. Ushirobira, D. Efimov, D. Tran and J.-C. Massabuau. ‘Velocity estimation of valve
movement in oysters for water quality surveillance’. In: IFAC-PapersOnLine 48 (2015), pp. 333–338.

[64] S. Aranovskiy, R. Ushirobira, D. Efimov and G. Casiez. ‘Frequency Domain Forecasting Approach
for Latency Reduction in Direct Human-Computer Interaction’. In: Proc. 56th IEEE Conference on
Decision and Control (CDC). Melbourne, 2017.

[65] E. Bernuau, D. Efimov, W. Perruquetti and A. Polyakov. ‘On Homogeneity and Its Application in

Sliding Mode’. In: Int. J. Franklin Institute 351.4 (2014), pp. 1866–1901.

[66] E. Bernuau, A. Polyakov, D. Efimov and W. Perruquetti. ‘Verification of ISS, iISS and IOSS properties

applying weighted homogeneity’. In: Systems & Control Letters 62 (2013), pp. 1159–1167.

[67] E. Bernuau, D. Efimov, W. Perruquetti and E. Moulay. ‘Robust finite-time output feedback stabiliza-
tion of the double integrator’. In: International Journal of Control 88.3 (2015), pp. 451–460.

[68] D. Efimov, W. Perruquetti and J.-P. Richard. ‘Development of Homogeneity Concept For Time-Delay

Systems’. In: SIAM Journal on Optimization and Control 52.3 (2014), pp. 1403–1808.

[69] D. Efimov, A. Polyakov, A. Levant and W. Perruquetti. ‘Realization and Discretization of Asymp-
totically Stable Homogeneous Systems’. In: IEEE Trans. Automatic Control 62.11 (2017), pp. 5962–
5969.

[70] D. Efimov, A. Polyakov, W. Perruquetti and J.-P. Richard. ‘Weighted Homogeneity for Time-Delay
Systems: Finite-Time and Independent of Delay Stability’. In: IEEE Trans. Automatic Control 61.1
(2016), pp. 210–215.

[71] D. Efimov and W. Perruquetti. ‘On conditions of oscillations and multi-homogeneity’. In: Mathem-
atics of Control, Signals, and Systems 28.1 (2015), pp. 1–37. URL: http://dx.doi.org/10.1007/s
00498-015-0157-y.

Project VALSE

21

[72] N. Espitia, A. Polyakov, D. Efimov and W. Perruquetti. ‘Boundary time-varying feedbacks for fixed-
time stabilization of constant-parameter reaction-diffusion systems’. In: Automatica 103 (2019),
pp. 398–407. URL: https://doi.org/10.1016/j.automatica.2019.02.013.

[73] M. Feingesicht, A. Polyakov, F. Kerhervé and J.-P. Richard. ‘SISO model-based control of separated
flows: Sliding mode and optimal control approaches’. In: International Journal of Robust and
Nonlinear Control 27.18 (2017), pp. 5008–5027.

[74] E. Leurent, D. Efimov, T. Raïssi and W. Perruquetti. ‘Interval Prediction for Continuous-Time
Systems with Parametric Uncertainties’. In: Proc. 58th IEEE Conference on Decision and Control
(CDC). Nice, 2019.

[75] F. Lopez-Ramirez, A. Polyakov, D. Efimov and W. Perruquetti. ‘Finite-time and Fixed-time Observer

Design: Implicit Lyapunov function approach’. In: Automatica 87.1 (2018), pp. 52–60.

[76] A. Polyakov. ‘Nonlinear feedback design for fixed-time stabilization of linear control systems’. In:

IEEE Transactions on Automatic Control 57(8) (2012), pp. 2106–2110.

[77] A. Polyakov, J.-M. Coron and L. Rosier. ‘On Homogeneous Finite-Time Control for Linear Evolution

Equation in Hilbert Space’. In: IEEE Transactions on Automatic Control (2018).

[78] A. Polyakov, D. Efimov and B. Brogliato. ‘Consistent Discretization of Finite-time and Fixed-time

Stable Systems’. In: SIAM Journal on Optimization and Control 57.1 (2019), pp. 78–103.

[79] A. Polyakov, D. Efimov, E. Fridman and W. Perruquetti. ‘On Homogeneous Distributed Parameter

Systems’. In: IEEE Trans. Automatic Control 61.11 (2016), pp. 3657–3662.

[80] A. Polyakov, D. Efimov and W. Perruquetti. ‘Finite-time and fixed-time stabilization: Implicit Lya-

punov function approach’. In: Automatica 51 (2015), pp. 332–340.

[81] H. Ríos, D. Efimov, J. A. Moreno, W. Perruquetti and J. G. Rueda-Escobedo. ‘Time-Varying Parameter
Identification Algorithms: Finite and Fixed-Time Convergence’. In: IEEE Transactions on Automatic
Control 62.7 (2017), pp. 3671–3678. URL: https://dx.doi.org/10.1109/TAC.2017.2673413.

[82] R. Ushirobira, D. Efimov and P.-A. Bliman. ‘Estimating the infection rate of a SIR epidemic model

via differential elimination’. In: Proceedings of ECC. Naples, 2019.

[83] R. Ushirobira, D. Efimov, G. Casiez, N. Roussel and W. Perruquetti. ‘A forecasting algorithm for
latency compensation in indirect human-computer interactions’. In: Proceedings of ECC. Alborg,
2016, pp. 1081–1086.

[84] K. Zimenko, D. Efimov, A. Polyakov and W. Perruquetti. ‘A note on delay robustness for homogen-

eous systems with negative degree’. In: Automatica 79.5 (2017), pp. 178–184.
<scratchpad>
- Main topic: Research Centre at the University of Lille, specifically the VALSE project
- Key points: VALSE project focuses on control and estimation problems in distributed systems, particularly in IoT and CPS
- Structure: The document is divided into sections, including project-team, activity report, research program, application domains, social and environmental responsibility, highlights of the year, new software, and scientific production
- Potential artifacts to ignore: web-related elements, unnecessary HTML tags, and formatting
</scratchpad>

<final_summary>
The VALSE project, conducted at the University of Lille, focuses on addressing control and estimation problems in distributed systems, particularly in the Internet of Things (IoT) and Cyber-Physical Systems (CPS). The project aims to develop control and estimation algorithms for CPS and IoT, with a focus on finite-time and fixed-time stability. The VALSE team has made significant progress in this area, with publications in top journals such as Automatica, IEEE Transactions on Automatic Control, and International Journal of Robust and Nonlinear Control. The project has also explored applications in various domains, including robotics, autonomous systems, and smart vehicles. Overall, the VALSE project is a comprehensive effort to advance control and estimation techniques in distributed systems, with potential impacts on various fields of engineering and science.
The VALSE project, conducted at the University of Lille, focuses on addressing control and estimation problems in distributed systems, particularly in the Internet of Things (IoT) and Cyber-Physical Systems (CPS). The project aims to develop control and estimation algorithms for CPS and IoT, with a focus on finite-time and fixed-time stability. The VALSE team has made significant progress in this area, with publications in top journals such as Automatica, IEEE Transactions on Automatic Control, and International Journal of Robust and Nonlinear Control. The project has also explored applications in various domains, including robotics, autonomous systems, and smart vehicles. Overall, the VALSE project is a comprehensive effort to advance control and estimation techniques in distributed systems, with potential impacts on various fields of engineering and science.