Distributed Optimal Leader-Following Consensus Control of MAS Under Input Saturation: A Stackelberg Game Approach

This article addresses the optimal state observation and leader-following consensus for a nonlinear multiagent system (MAS) with input saturation under the Stackelberg game framework. The dynamics and states of followers are unknown, the leader's dynamics is unknown, and the leader's state is accessible only to a subset of followers. First, a distributed estimation algorithm is developed for each follower to estimate the leader's state. Then, a game-based observer is designed to estimate the follower state, where the bidirectional interaction between the observer and follower dynamics is considered. The follower dynamics and observer are modeled as leader and follower players in the Stackelberg game, respectively. Based on the proposed structure, an optimal auxiliary controller for the observer and an optimal consensus controller are developed. Furthermore, a fuzzy reinforcement learning approach approximates the unknown dynamics and derives the optimal state observers and leader-following consensus controllers. All closed-loop signals are guaranteed to be uniformly ultimately bounded based on the Lyapunov method. Finally, simulations are provided to validate the effectiveness of the proposed approach.