Luận án TS: Điều khiển hợp tác hệ đa tác tử mạng cụm - ĐH Reims Champagne-Ardenne

UNIVERSITÉ DE REIMS CHAMPAGNE-ARDENNE ÉCOLE DOCTORALE SCIENCES DU NUMERIQUE ET DE L’INGENIEUR n°620 THÈSE Pour obtenir le grade de DOCTEUR DE L’UNIVERSITÉ DE REIMS CHAMPAGNE-ARDENNE Discipline : Automatique, signal, productique, robotique Spécialité :Automatique Présentée et soutenue publiquement par VAN THIEM PHAM Le 14 janvier 2021 Cooperative Control of Multi-Agent Systems in the Clustered Network JURY M. Noureddine MANAMANNI, Professeur, Université de Reims Champagne Ardence, Directeur de thèse M. Nadhir MESSAI, Maître de Conférences HDR, Université de Reims Champagne Ardence, Co-Directeur de thèse M. Frederic KRATZ, Professeur, INSA Centre VAL DE LOIRE, Rapporteur M.

DJOUADI, Professeur, University of Tennessee, Rapporteur M. Michel BASSET, Professeur, Université de Haute-Alsace, Examinateur, Président du jury Mme Lydie NOUVELIERE, Maître de Conférences HDR, Université d’Evry, Examinateur i Acknowledgements Obtaining a Ph. degree in Electrical and Computer Engineering at URCA (University of Reims Champagne-Ardenne) is my ultimate goal during the last four years. Along my journey, I am proud to be a member of CReSTIC, where I have been very fortunate to interact with many great people.

Noureddine MANAMANNI, and my Ph. co-advisor, Prof. Nadhir MESSAI ob- viously play a signicant role in my success at CReSTIC. During my time working under their supervision, Noureddine and Nadhir showed me their constant guidance and support for my studies and career.

They taught me how to conduct research, how to write a paper, and above all how to shape my career. Whenever I seek advice, they have always been there with the best solution. I am thankful and indebted for their great care and concern about my career and my family. My deep thanks to all my friends and colleagues, who gave me unforgettable and precious friendship, crossed the barriers of language and culture and who were always present in good times as well as in the most dicult.

Dinh Hoa Nguyen and Prof. Thinh Thanh Doan for our collaborations during my last semester here. I would also like to extend my sincere thanks to all the members of the jury for agreeing to review my presentation, despite their busy schedule. My sincere appreciation to Prof.

Lydie NOUVELIERE and Prof. Michel BASSET, who do me the honor of examining this work. I also express my deep thanks to Prof. Frederic KRATZ and Prof.

DJOUADI, for agreeing to evaluate this work. I thank the VIED (Vietnamese International Education Department) of MOET (Ministry of Education and Training) for their nancial support through my assis- tantship and fellowship during my Ph. Most importantly, I thank my family for their unconditional love and unlimited support for my career success. I extremely appreciate my mother-in-law for being here in 6 months to take care of my kids, so that I would have more time for my studies.

I also thank my kids, Gia Binh, and Nhat Nam (Kévin) for the time taken from them. They are always a big motivation to push me forward. I wish to thank my wife, Thanh Quynh, for being with me and showing her constant support for my career. She has also been very patient with all of my frustrations during my studies.

I wish to show my gratitude and love to my parents for their unlimited support of my career choice. They have worked very hard and given up many things to make my success possible. This thesis is dedicated to them. iii Contents Acknowledgements i List of Notations vii General Introduction 9 1 An Overview and Open Research Questions 17 1.1 An Overview on Cooperative Control of MASs .1 Dynamics of MASs .3 Constraints in MASs .1 Cluster networks and MAS .2 Open Research Questions.

38 2 Impulsive Observer-Based Control in Clustered Network 41 2.1 Related Work and Contributions .1 Impulsive Observer-based Control .3 Agreement Behavior Analysis .1 Local Agreement Behavior .2 Global Agreement Behavior .4 Impulsive Observer-Based Consensus Controller .2 Impulsive Observer-Based Control Design .3 Target Enclosing Problem .1 The Global Consensus Value .2 Illustrative Example of Problem 2 .3 Application to Target Enclosing of UAVs. 69 3 Robust Formation Control Under State Constraints 71 3.1 Related Work and Contributions .1 Robust Formation Control .2 Useful Assumptions and Lemmas .3 Robust Distributed Formation Design .2 Formation Analysis in Clustered Network .3 Robust Stabilization Controller Design .4 Application to Formation of UAVs. 96 4 Output Consensus of Heterogeneous MASs under Disturbances 97 4.1 Related Work and Contributions .1 Output Consensus Control .3 Consensus of the Virtual Reference Systems .2 Consensus Analysis in Clustered Network .3 Stabilization Controller Design .4 Output Consensus of the Heterogeneous Agents. 119 5 Conclusion and Future Research Directions 121 5.3 Suggested Future Research .2 Positive denite and negative denite matrices .6 Gershgorin circle theorem .7 Linear Matrix Inequality (LMI) .8 Sector nonlinearities and S-procedure.

131 B Basic Algebraic Graph Theory 133 B.2 Graph-related matrices .3 Eigenstructure of Laplacian matrix .4 Ger²gorin circle criterion. 137 Bibliography 139 v List of Figures 1 Statistiques d'un certain nombre d'articles relatifs au "consensus, coopéra- tive, MASs" dans les revues entre 2005  Juillet, 2020. 1 2 Statistiques du pourcentage d'articles liés textit "consensus, coopérative, MASs" dans les revues au cours de 2005  Juillet, 2020. 2 3 Chronologie du contrôle coopératif majeur de MAS.

3 4 Communications en ondes millimétriques 5G pour les réseaux sans l 2 assistés par des drones. 4 3 5 Le réseau social. 4 6 Aperçu général de la thèse et des principales contributions. 5 7 Statistics of a number of papers related "consensus, cooperative, MASs" in Journals during 2005  July, 2020.

9 8 Statistics of percentage of papers related"consensus, cooperative, MASs" in Journals during 2005  July, 2020. 10 9 Timeline of the major cooperative control of MAS. 11 5 10 5G mmWave communications for UAV-assisted wireless networks. 12 6 11 The social network.

12 12 General overview of the thesis and main contributions .1 The research framework of cooperative control of MASs.2 The research framework of dynamics of MASs.3 The research framework of network topology of MASs.4 The research framework of contraints of MASs.5 The research framework of cooperative control of MASs.6 The clustered network of 15 agents .1 The communication of the network.2 a) The state of agents in each cluster; b) Combinational error E8 with dierent impulsive interval.3 Convergence of the new variable ψi .4 The rst state curve of agents xi1 in the clustered network.5 The state curve of agents xi2 , xi3 in the clustered network .6 Convergence of observation error ei of agents in the clustered network.7 a) The Lyapunov function V in (2.54), b) Combinational error E8 with dierent ∆.8 Formation of ten UAVs'positions encloses the target.1 The scheme of formation problem .2 State formation of six agents moving in the XY plane .3 The communication of the network .4 Pentacle formation of ten UAVs'positions without communication network of leaders.5 A reset signal and leaders' states of UAVs .6 Convergence of the variable ψ2 and the Lyapunov function.7 Ten-UAVs'positions (xi , yj ) constraints (left) and ten-UAVs'velocities (vxi , vyi ) constraints (right).8 Pentacle formation of ten UAVs'positions (xi , yi ) (lower) and consen- sus of ten UAVs'velocities (vxi , vyi ) under state constraints (upper).9 Ten-UAVs' positions (xi , yj ) under state constraints belonging to [−15 15](m) (upper); Ten-UAVs' positions (xi , yj ) under state constraints belong- ing to [−3 3](m) (lower).10 Ten-UAVs' velocities (vxi , vyi ) under state constraints belonging to [−15 8](m/s) (upper); Ten-UAVs' velocities (vxi , vyi ) under state con- straints belonging to [−3 3](m/s) (lower).1 The heterogeneous MASs are in the physical space while internal reference models are generated from a cyber command center through the virtual clustered network.2 The states of internal reference models vi , the new variable ψ2 .3 The states of of internal reference model vi1 with dierent α.4 E = ψ2T ψ2 with dierent α.5 Estimated states x̂2 , estimated disturbance dˆ1 , estimated disturbance error edi , and observation error exi .6 The output of agent yi and the disagrement vector ei .1 Dierent types of graphs of ve nodes: a) an undirected connected graph, b) a strongly connected graph, c) a balanced and strongly connected graph, d) a directed spanning tree.2 Ger²gorin disks of L in the complex plane. 138 vii List of Notations C Set of complex numbers R Set of real numbers Z+ Set of positive integer numbers Fm×n Set of matrices with m rows, n columns, and entries in R or C Rm×n Set of matrices with m rows, n columns, and entries in R x ∈ Rnx Real-valued column vector of dimension nx x∗ The conjugate transpose of x t Continuous-tiem instant, real-valued x(t) Continuous time-variant vector variable xi (t) Continuous time-variant vector variable of agent i kxkp The p-norm of vector x, for p ≥ 1 |N i | Cardinality of the set N i aij The entry at the position of ith row and j th column of matrix A AT Transpose of matrix A AH Hermitian conjugate of matrix A ∈ C n×m A∗ Hermitian transpose or conjugate transpose of matrix A A>0 Positive denite matrix A A≥0 Positive semi-denite matrix A A<0 Negative denite matrix A A≤0 Negative semi-denite matrix A det(A) Determination of matrix A rank(A) Rank of matrix A ker(A) Kernel of matrix A A⊗B Kronecker product of matrices A and B I Identity matrix with appropriate dimensions 0 Zero matrix with appropriate dimensions , Equals by denition z̄ Conjugate of z ∈ C   A1. , where Ai ∈ Fni ×mi diag(A1 ,. , An ) Block-diagonal matrix .

An ix List of Abbreviations MASs Multi Agent Systems UAVs Unmaned Atutonous Vehilces LMIs Linear Matrix Inequalities CPS Cyber Physical Systems NCS Network Control Systems LQR Linear Quadratic Reguarator 1 Introduction Générale Au cours des dernières décennies, les progrès rapides de la science et des sciences et des technologies de l'information et de la communication ont rendu possible le déploiement d'un grand nombre d'agents autonomes qui travaillent en coopération pour assurer des missions civiles et militaires. Comparativement à un seul agent complexe, cela peut améliorer considérablement l'ecacité opérationnelle, réduire les coûts et fournir des degrés supplémentaires de redondance. Le fait plusieurs agents autonomes pour travailler ensemble ecacement an d'obtenir des comportements collectifs de groupe est généralement appelé contrôle coopératif des systèmes multi- agents (MASs). Le contrôle coopératif des MASs a fait l'objet d'une attention particulière de la part de diverses communautés scientiques, en particulier de la communauté des systèmes et du contrôle.

Figure 1: Statistiques d'un certain nombre d'articles relatifs au "consensus, coopérative, MASs" dans les revues entre 2005  Juil- let, 2020 An de conrmer ce constat, nous avons analysé les données des articles publiés dans certaines revues de qualité Q1 au cours de la période 2005 - juillet 2020 avec les mots clés "consensus, cooperative, MASs", le résultat de ce travail est illustré par la Fig.1, qui montre que le sujet du "contrôle coopératif" est de plus en plus étudié. Par exemple, le nombre d'articles dans "Automatica" en 2015 augmente de 30 fois par rapport à 2005, tandis que les publications "IEEE Trans" augmentent d'environ 10 fois. En outre, de plus en plus d'applications potentielles dans divers domaines tels que le vol en formation, l'informatique distribuée, la robotique, la surveillance, les systèmes de reconnaissance, les systèmes d'alimentation électrique, l'attaque coopérative de plusieurs missiles et les systèmes de transport intelligents sont analysées. En particulier, 31% des articles publiés dans Automatica représen- tant une proportion importante (voir Fig.

Ensuite, 23%, 18%, 15%, et 13% sont respectivement le pourcentage d'articles publiés dans "International Journal Con- trol", "IEEE Trans", "IET Control Theory & Applications", et "System Control & 2 Letters".