Distributed Reinforcement Learning Optimal Cluster Consensus Control for Takagi-Sugeno Fuzzy Multi-Agent Systems

This paper studies the distributed optimal cluster consensus control problem with a data-driven value iteration (VI) algorithm for Takagi-Sugeno (T-S) fuzzy multi-agent systems (MASs) with unknown system dynamics. In distributed optimal cluster consensus control design, we view each agent’s control policy and its neighboring followers’ control policy as rival players, then a fuzzy distributed optimal cluster consensus control policy is proposed by applying differential graphical game theory and acyclic partition. Since the analytical optimal cluster consensus control solutions are reduced to solving the distributed game algebraic Riccati equations (GAREs), which is difficult to obtain their analytical solutions, a data-driven VI algorithm is presented. It is proved that the developed algorithm can converge to the approximation solutions of optimal controllers, and the proposed fuzzy distributed optimal cluster consensus control scheme not only guarantees the followers in each cluster to asymptotically track their corresponding leaders but also achieves the Nash equilibrium of differential graphical game. Finally, we apply the developed fuzzy distributed optimal cluster consensus control method with a data-driven VI algorithm to multiple nonlinear unmanned surface vehicle (USV) systems, the computer simulation results verify the effectiveness of the developed optimal control approach.