Optimal Containment Control of Heterogeneous Multiagent Systems With Unknown Dynamics and Actuator Faults via Fuzzy Reinforcement Learning

This article investigates the fuzzy optimal fault-tolerant containment control (FTCC) problem for heterogeneous nonlinear multiagent systems with unknown dynamics and actuator faults in which the unknown dynamics exhibit nonlinear behavior. To address this problem, a performance index comprising local containment error, control energy, and fault effects, is first formulated under the zero-sum differential game, where controllers and faults are treated as opposing players with different signs. Subsequently, improved generalized fuzzy hyperbolic model-based approximation techniques are used to identify unknown dynamics and learn optimal FTCC policies incorporating reinforcement learning (RL). Specifically, to enhance the weight convergence performance and relax the traditional persistence of excitation condition, a practical fixed-time identifier is developed based on the generalized fuzzy hyperbolic model by integrating practical fixed-time system identification technique with experience replay technique. Then, using the generalized fuzzy hyperbolic model as the critic, a fuzzy-RL algorithm with experience replay is developed to learn optimal FTCC policies from the coupled Hamilton–Jacobi–Isaacs equations. The containment error and the critic approximation error are ensured to be ultimately uniformly bounded using the Lyapunov method. Finally, the validity of the control scheme is verified via a numerical simulation.