Decentralized Control for Guaranteed Individual Costs in a Linear Multi-Agent System: A Satisfaction Equilibrium Approach

Abstract

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.