Commande sous contraintes de systèmes dynamiques multi-agents 0.5cm Control of Multi-Agent

250 Pages·2012·6.45 MB·French

by  Ionela Prodan

Order no.: 2012-19-TH
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THESE DE DOCTORAT
DOMAINE : STIC
SPECIALITE : AUTOMATIQUE
Ecole Doctorale « Sciences et Technologies de l’Information des
T´el´ecommunications et des Syst`emes »
Pr´esent´ee par :
Ionela PRODAN
Sujet :
Commande sous contraintes de syst`emes dynamiques multi-agents
Soutenue le 3/12/2012
devant les membres du jury :
M. Georges BITSORIS U. Patras, Gr`ece Invit´e
M. Patrick BOUCHER SUPELEC, France Examinateur
Mme. Eva CRUCK DGA, France Examinatrice
M. Fernando FONTES FEUP, Portugal Invit´e
M. Morten HOVD NTNU, Norv`ege Rapporteur
M. St´ephane LE MENEC EADS, France Invit´e
M. Rudy NEGENBORN TU Delft, Pays Bas Examinateur
M. Silviu-Iulian NICULESCU CNRS-SUPELEC, France Co-encadrant
M. Sorin OLARU SUPELEC, France Directeur de th`ese
M. Fernando PEREIRA FEUP, Portugal Rapporteur
Mme. Cristina STOICA SUPELEC, France Co-encadrante

Thanks
The work presented in this thesis was conducted as a collaboration between the Au-
tomatic Department of Sup´elec and the Laboratory of Signals and Systems of CNRS-
Sup´elec, with funding from the EADS Foundation. During these last three years I have
succeeded to accomplish my objectives due to the help, support and friendship of many
people. I would like to take this opportunity to express again all my gratitude to each
one of them.
First of all, I wish to thank my supervisor, Professor Sorin Olaru for his effort in guiding
me in all research issues, his enthusiasm for research and his academic support. To him
and to my co-supervisors Assistant Professor Cristina Stoica and Professor Silviu-Iulian
Niculescu I am grateful for their help and continuous encouragement to explore new
research challenges and pursue them successfully.
I thank to Professor Patrick Boucher, the former Head of the Automatic Department for
welcoming me in the laboratory and for making sure that my thesis is developing in an
optimal way. Beyond these aspects, I am honored by the interest he has always shown
for my work and his presence in my thesis committee as the president of the jury. I am
thankfultoProfessorDidierDumur, thecurrentHeadoftheAutomaticDepartmentand
alltheprofessorsinthedepartmentfortheirconstantsupport. Furthermore,Iwouldlike
to thank Ms Marie-Claire Certiat who has regularly attended my work as representative
of the EADS Foundation and for her encouragement.
My deepest appreciation goes also to all the other members that agreed to be part of
the committee: Professor Morten Hovd, Professor Fernando Pereira, Research Engineer
Eva Cruck, Associate Professor Rudy Negenborn, Professor Georges Bitsoris, Professor
FernandoFontesandResearchEngineerSth´epaneLeMenec. Inparticular,Iamgrateful
ii
to the reviewers Professor Morten Hovd and Professor Fernando Pereira for their careful
reading of the manuscript and all the provided remarks which helped in improving the
overall quality of the exposition.
During these three years I had the chance to work with a large number of people and to
visit different laboratories. In particular, I thank Professor Georges Bitsoris, Professor
Jo˜ao Sousa, Dr. Ricardo Bencatel, Professor Fernando Fontes for the fruitful discussions
I had with them. Also, I enjoyed working with Dr. Florin Stoican and I have benefited
greatly from the clarity of vision he brings to his work. I am most grateful for the time
I spent at the Underwater Systems and Technology Laboratory from the University of
Porto in Portugal, a collaboration initiated by my supervisor. I enjoyed there everyone’s
friendliness and support, in particular Catarina Morais who I thank for giving up a few
hours from her schedule to show me the beautiful city of Porto. Thanks to Professor
Jo˜ao Sousa I had the chance to go at the Portuguese Air Force Academy, OTA, for the
flight experiments, which proved to be a unique experience for me. Also, I would like to
thank Professor Anders Rantzer for giving me the privilege to spend some time in the
Automatic Department from University of Lund in Sweden.
When I look back during my scientific study, I am grateful to many, many people who
have given me challenges and believed in my competence. My thanks go to Professor
Cristian Oara and Professor Radu Stefan from University “Polithenica” of Bucarest, as
well as to my highschool math professor Iuliana Turcu.
My warmest thanks go to my friends and colleagues: Vali, Catalin, Emanuel, Georgi,
Florin, Ana, Warody, Safta, Anca, Nam, Nikola, Andreea, Daniel, Julien, Antoine,
Christophe, Stefan, Dorin, Adriano, Raluca, Bogdan, Cristina, Ali.
I would not be here if it wasn’t for my parents, to whom I owe the greatest debt of
gratitude. I am also blessed to have my sisters Daniela and Iuliana, my life together
with them is an enormous joy, and it is, above all, my greatest source of strength. This
work is dedicated to them.
Pentru surorile mele Daniela si Iuliana,
parintilor mei.
******
“Satisfaction lies in the effort, not in the attainment; full effort is full victory.”
Mahatma Gandhi

E´COLE SUPE´RIEURE D’E´LECTRICITE´
Abstract
SPECIALITE : AUTOMATIQUE
Doctorate degree
by Ionela Prodan
The goal of this thesis is to propose solutions for the optimal control of multi-agent
dynamical systems under constraints. Elements from control theory and optimiza-
tion are merged together in order to provide useful tools which are further applied to
different problems involving multi-agent formations.
The thesis considers the challenging case of agents subject to dynamical constraints.
When designing control decisions, it becomes thus natural to take into account not only
exogenous factors (e.g., obstacles, reference tracking, etc.) but also the internal (state)
dynamics of the agents and their structural properties (as settle-time or nonholonomic
characteristics).
To deal with these issues, well established concepts like set-theory, differential flatness,
Model Predictive Control (MPC), Mixed-Integer Programming (MIP) are adapted and
enhanced. Using these theoretical notions, the thesis concentrates on understanding
the geometrical properties of the multi-agent group formation and on providing a novel
synthesis framework which exploits the group structure. In particular, the formation
design and the collision avoidance conditions are casted as geometrical problems and
optimization-based procedures are developed to solve them. Moreover, considerable ad-
vances in this direction are obtained by efficiently using MIP techniques (in order to
derive an efficient description of the non-convex, non-connected feasible region which
results from multi-agent collision and obstacle avoidance constraints) and stability prop-
erties (in order to analyze the uniqueness and existence of formation configurations).
The existence and uniqueness of a tight formation of agents is further linked with con-
straints over the eigenstructure of the state matrices of the agents.
Lastly, some of the obtained theoretical results are applied on a challenging practical
application. A novel combination of MPC and differential flatness (for reference gener-
ation) is used for the flight control of Unmanned Aerial Vehicles (UAVs).
E´COLE SUPE´RIEURE D’E´LECTRICITE´
R´esum´e
SPECIALITE : AUTOMATIQUE
Diplˆome de doctorat
par Ionela Prodan
L’objectif de cette th`ese est de proposer des solutions aux probl`emes li´es `a la com-
mande optimale de syst`emes dynamiques multi-agents en pr´esence de contraintes.
Des ´el´ements de la th´eorie de commande et d’optimisation sont appliqu´es `a diff´erents
probl`emes impliquant des formations de syst`emes multi-agents.
La th`ese examine le cas d’agents soumis `a des contraintes dynamiques. Il devient donc
naturel de tenir compte non seulement des facteurs exog`enes (par exemple les obstacles,
le suivi de r´ef´erence, etc.), mais aussi de la dynamique interne (l’´etat) d’agents et de
leurs propri´et´es.
Pourfaireface`acesprobl`emes,lesconceptsbien´etablistelsquelath´eoriedesensembles,
la platitude diff´erentielle, la commande pr´edictive (Model Predictive Control - MPC),
la programmation mixte en nombres entiers (Mixed-Integer Programming - MIP) sont
adapt´es et am´elior´es. En utilisant ces notions th´eoriques, ce travail de th`ese a port´e
sur les propri´et´es g´eom´etriques de la formation d’un groupe multi-agents et propose un
cadre de synth`ese original qui exploite cette structure.
En particulier, le probl`eme de conception de formation et les conditions d’´evitement
des collisions sont formul´es comme des probl`emes g´eom´etriques et d’optimisation pour
lesquels il existe des proc´edures de r´esolution. En outre, des progr`es consid´erables dans
ce sens ont ´et´e obtenus en utilisant de fa¸con efficace les techniques MIP (dans le but
d’end´eduireunedescriptionefficacedespropri´et´esdenonconvexit´eetdenonconnexion
d’une r´egion de faisabilit´e r´esultant d’une collision de type multi-agents avec des con-
traintes d’´evitement d’obstacles) et des propri´et´es de stabilit´e (afin d’analyser l’unicit´e
et l’existence de configurations de formation de syst`emes multi-agents). L’existence et
l’unicit´e d’une formation ´etroite d’agents sont, en outre, li´ees `a des contraintes sur la
structure propre des matrices d’´etat des agents.
Enfin, certains r´esultats th´eoriques obtenus ont ´et´e appliqu´es dans un cas pratique tr`es
int´eressant. Onutiliseunenouvellecombinaisondelacommandepr´edictiveetdelaplat-
itude diff´erentielle (pour la g´en´eration de r´ef´erence) dans la commande et la navigation
de v´ehicules a´eriens sans pilote (UAVs).
Syst`emes dynamiques multi-agents du point de vue de la
commande th´eorique
Toutd’abord, afindepercevoirlesb´en´eficesretir´esdel’emploidessyst`emesmulti-agents
dans l’ing´enierie de la commande, il est n´ecessaire de s’attarder un peu sur la d´efinition
de ces syst`emes. Il existe plusieurs d´efinitions d’un agent, ce qui est duˆ principalement `a
l’universalit´e de ce mot et au fait qu’il ne peut pasˆetre propre `a une seule communaut´e.
La plupart des d´efinitions proviennent de la communaut´e informatique et ils ont tous
trois concepts de base : la notion d’agent, de son environnement et de son autonomie.
La d´efinition suivante est souvent cit´ee : “un agent est une entit´e mat´erielle ou logicielle
qui se trouve dans un certain environnement, et qui est capable d’actions autonomes
dans l’environnement afin de r´epondre `a ses objectifs”. Comme l’indique la d´efinition,
les agents sont soit des entit´es physiques (mat´erielles), ce qui est le cas des robots, des
v´ehicules ou des pi´etons, dans un environnement physique (par exemple, un syst`eme de
commande),soitdesentit´esvirtuellesdansunenvironnementinformatique(parexemple,
des sources de donn´ees, des sources informatiques), ce qui est le cas des agents logiciels.
Cependant, dans le contexte des agents de commande, seul le premier cas est int´eressant