Adaptive Fixed-Time Observer-Based Fuzzy Fault-Tolerant Containment Control for Stochastic Fully Heterogeneous Nonlinear Systems

This article addresses the adaptive fuzzy fault-tolerant output containment control of fully heterogeneous nonlinear multiagent systems subject to stochastic disturbances, where not only followers but also leaders are equipped with nonidentical dynamics. First, fully distributed fixed-time observers are designed to observe active leaders' information including system matrices, positions, and external inputs, which are only accessible to a limited group of followers. Subsequently, adaptive algorithms are utilized, informed by the observations of leaders' system matrices, to solve the regulator equations. Then, the state observer-based controller is proposed, which employs the adaptive fuzzy-based approximation law to approximate the unknown nonlinear item and integrates the adaptive gains to cope with the actuator faults in the follower's dynamics. In addition, a set of modest conditions and rigorous proofs is constructed to guarantee the accomplishment of predetermined output containment through the output regulation method and Lyapunov stability theory. Finally, the theoretical analysis is validated through performing a numerical simulation.