Distributed Differential Games for Control of Multi-Agent Systems

Motivated by the challenges arising in the field of multi-agent system (MAS) control, we consider linear heterogeneous MAS subject to local communication and investigate the problem of designing distributed controllers for such systems. We provide a game theoretic framework for systematically designing distributed controllers, taking into account individual objectives of the agents and their possibly incomplete knowledge of the MAS. Linear state-feedback control laws are obtained via the introduction of a distributed differential game, namely, the combination of local non-cooperative differential games, which are solved in a decentralized fashion. Conditions for stability of the MAS are provided for the special cases of acyclic and strongly connected communication graph topologies. These results are then exploited to provide stability conditions for general graph topologies. The proposed framework is demonstrated on a tracking synchronization problem associated with the design of a distributed secondary voltage controller for microgrids and on a numerical example.

Automated summary

Motivated by challenges in multi-agent system control, this study investigates the design of distributed controllers for linear heterogeneous systems subject to local communication. A game theoretic framework is proposed, taking into account individual agent objectives and incomplete knowledge. Linear state-feedback control laws are obtained through a distributed differential game, solved in a decentralized manner. Stability conditions are provided for specific communication graph topologies and then applied to general graph topologies.