Decentralized control for guaranteed individual costs in a linear multi-agent system: A satisfaction equilibrium approach

Jomphop Veetaseveera (1) , Vineeth S. Varma (1) , Irinel-Constantin Morarescu (1) , Jamal Daafouz (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

This work focuses on the design of decentralized feedback control gains that aims at optimizing individual costs in a multi-agent synchronization problem. As reported in the literature, the optimal control design for synchronization of agents using local information is NP-hard. Consequently, we relax the problem and use the notion of satisfaction equilibrium from game theory to ensure that each individual cost is guaranteed to be lower than a given threshold. Our main results provide conditions in the form of linear matrix inequalities (LMIs) to check if a given set of control gains are in satisfaction equilibrium i.e. all individual costs are upper-bounded by the imposed threshold. Moreover, we provide an algorithm in order to synthesize gains that are in satisfaction equilibrium. Finally, we illustrate this algorithm with numerical examples.

Mots clés: Multi-agent systems; Synchronization; Decentralized control; Optimal control; Games

Domaines: Automatique

Jomphop Veetaseveera, Vineeth S. Varma, Irinel-Constantin Morarescu, Jamal Daafouz. Decentralized control for guaranteed individual costs in a linear multi-agent system: A satisfaction equilibrium approach. IEEE Control Systems Letters, 2019, 3 (4), pp.918-923. ⟨10.1109/LCSYS.2019.2919425⟩. ⟨hal-02390663⟩