Séminaire de l'action Commande décentralisée des systèmes multi-agents sous contraintes le 10 Mars 2023 au CNAM à Paris. Inscription gratuite mais obligatoire. L’action sollicite également les collègues pour recenser les travaux de recherche sur ce thème. Lien vers le sondage.

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**Programme de la réunion du Vendredi 10 Mars, 10h00 - 16h00**

**Lieu : **CNAM, 292 Rue Saint Marin, 75013 Paris, Salle 11A1-39 (Accès 11, Premier étage)

**10:00-10:15 : Présentation de l’action MACs (commande décentralisée des systèmes multi-agents sous contraintes) **

**10:15-10h55 : Exponential Bipartite Containment Tracking over Signed Networks with Multiple Leaders**

**Auteurs : **Pelin Sekercioglu (ONERA & L2S, Université Paris-Saclay), Elena Panteley (L2S, Univ. Paris-Saclay), Ioannis Sarras (ONERA), Antonio Loria (L2S) et Julien Marzat (ONERA).

**Résumé** : In the study of coordination of multiagent networks, a large number of consensus problems have been studied. In a network consisting of a leader, all followers converge to the leader’s states and achieve consensus. On the other hand, in networks containing more than one leader, it is more appropriate to speak of containment control, which consists in making all followers’ states converge to a convex hull determined by the leaders’ initial states. However, when the network contains multiple leaders and interactions with signed weights, the containment objective is no more achievable. For this case, we address the distributed bipartite containment tracking-control problem for autonomous vehicles described by first and second-order systems, and steered by multiple cooperative and competitive leaders. Because of the existence of multiple leaders and antagonistic interations, the followers’ states converge to a residual compact set determined by the cooperative leaders’ initial conditions and competitive leaders’ symmetric initial conditions. For this bipartite containment set, we establish global exponential stability and we compute the exact equilibria to which all agents converge. We provide strict Lyapunov functions and establish robustness with respect to external disturbances. Finally, we present some first results on the distributed control of a multiagent system interconnected over a signed undirected network and we suppose that agents must keep a certain distance from each other to avoid inter-agent collisions. In order to take into account these constraints, we base our control law on the gradient of a barrier Lyapunov function.

**10:50-11:30 : Space-time budget allocation policy design for viral marketing**

**Auteurs : **Constantin Morarescu (CRAN, Univ. Lorraine)

**Résumé** : We address formally the problem of opinion dynamics when the agents of a social network (e.g., consumers) are not only influenced by their neighbors but also by an external influential entity referred to as a marketer. The influential entity tries to sway the overall opinion as close as possible to a desired opinion by using a specific influence budget. We assume that the exogenous influences of the entity happen during discrete-time advertising campaigns; consequently, the overall closed-loop opinion dynamics becomes a linear-impulsive (hybrid) one. The main technical issue addressed is finding how the marketer should allocate its budget over time (through marketing campaigns) and over space (among the agents) such that the agents’ opinion be as close as possible to the desired opinion. Our main results show that the marketer has to prioritize certain agents over others based on their initial condition, their influence power in the social graph and the size of the cluster they belong to. The corresponding space-time allocation problem is formulated and solved for several special cases of practical interest. Valuable insights can be extracted from our analysis. For instance, for most cases, we prove that the marketer has an interest in investing most of its budget at the beginning of the process and that budget should be shared among agents according to the famous water-filling allocation rule. Numerical examples illustrate the analysis.

**11:25-12:05 : Commande homogène et robustesse des systèmes multi-agents échantillonnés**

**Auteurs : **Patrick Coirault (LIAS, Univ. Poitiers) et Emmanuel Moulay (XLIM, Univ. Poitiers), Tomas Menard (LAC, UNICAEN)

**Résumé** : The first part of this talk is devoted to homogeneous control design for sampled data multi-agent systems. The second part focusses on the robust properties of sampled data multi-agent systems.

**13:30-14:10 : Distributed predefined-time optimization in multi-agent systems and ROS-based multi agent systems control architecture **

**Auteurs : **Pablo De Villeros (LAMIH, UPHF), Michael Defoort (LAMIH, UPHF), Mohamed Djemai (LAMIH, UPHF)

**Résumé** : The first part of this talk is devoted to distributed predefined-time optimization in multi-agent systems. With the development of distributed computing and large-scale networks during the past decade, consensus-based distributed optimization has become a highly active subject in control engineering due to its application in different areas, such as resource allocation, smart grids, sensor networks and machine learning. Additionally, in some applications of motion coordination, it is desirable that multiple physical agents establish a particular formation around a location, which is optimal for the whole team. However, most existing methods do not sufficiently take time as a constraint and do not always exhibit a reasonable convergence rate. In this presentation, we give a brief description of the different algorithms in the current literature, in terms of their convergence rates (asymptotic/exponential, finite-time, fixed-time, predefined-time). We describe a novel distributed optimization algorithm for multi-agent systems with several salient features: predefined-time convergence, it can be used on undirected graphs and detail-balanced graphs and it requires few adjustable parameters, without the need of sharing the gradients and Hessians among agents.

The second part of this talk is devoted to a ROS-based architecture developed for testing and demonstration of decentralized control algorithms designed for multi-agent systems. Aimed at bridging a gap between theory and practical deployment of cooperative control schemes, this architecture provides a simulator with multi-agent systems having mobile robot agents.

**14:10-14:50 : Synchronization enforcement, emergent behaviors, and its application.**

**Auteurs : **Jin Gyu Lee (INRIA,Lille)

**Résumé** : This work mainly relies on strong coupling, to enforce synchronization. The benefit is the emergence of new behaviors in the network as a collective one, which may not be able to be performed by individuals. Our belief is that for achieving such an objective in a collaborative sense, synchronization enforcement is somewhat needed. An illustration of this belief will be the first part of my talk utilizing some of the example networks, e.g., a network that performs distributed estimation which is resilient to sensor attacks. The second part will explore a little bit on different emergent behaviors that appear for non-linear coupling laws and for different types of synchronization enforcement.

**14:50-15:30 : Discussion et prospectives sur l’action **