Stackelberg Game-Based Finite-Horizon Optimal Fault-Tolerant Control of Heterogeneous MASs

This article investigates the problem of finite-horizon optimal fault-tolerant control for heterogeneous nonlinear discrete-time multiagent systems. A distributed optimal fault estimation and optimal fault-tolerant control scheme is presented based on the Stackelberg game and graphical game frameworks, in which agent systems and corresponding fault estimators are treated asthe “leader” and “follower” in the Stackelberg game, and the agent systems constitutes a graphical game. This is more general than the existing integration design of fault estimation as well as fault-tolerant control, as it better reveals the interaction between the agent system and its fault estimator. To achieve interactive Stackelberg equilibrium, an auxiliary controller for fault estimator is designed, which exhibits non cooperative properties with the fault-tolerant controller of the agent. Then, a finite-time distributed estimator for discrete-time case is developed for the first time to rapidly estimate the matrix and state of the leader agent. The coefficient matrices of the considered fault signals obey a hidden semi-Markov switching rule, which can encompass the existing actuator and sensor fault models. Further, two critic neural networks are established to obtain approximate solutions of interactive Stackelberg equilibrium online by employing the adaptive dynamic programming technology. Finally, simulation examples are provided to verify the efficacy and applicability of the proposed scheme.