Adaptive Fuzzy Fault-Tolerant Formation Control of High-Order Fully Actuated Multi-Agent Systems with Time-Varying Delays

The adaptive fuzzy fault-tolerant formation control of nonlinear high-order fully actuated multi-agent systems is studied in this paper, which contains time-varying delays and nonlinear non-affine faults. In contrast to the state-space approach, the proposed control method is based on the fully actuated system approach, which does not require converting a high-order system into a first-order one but directly designs controllers for high-order nonlinear multi-agent systems. The time-varying delays of the systems can be solved using the finite covering lemma and fuzzy logic systems. Compared with the traditional Lyapunov–Krasovskii functional method, the proposed control methodology relaxes the constraint of bounded derivatives for time-varying delays. The problem of algebraic loop in controller design caused by nonlinear non-affine faults is avoided using a Butterworth low-pass filter. Based on the Lyapunov stability theory, the proposed controller methodology is demonstrated to ensure the stability of the closed-loop system, and all followers can keep ideal formation with the leader. Finally, the validity of the theoretical results is demonstrated through three simulation examples, and the design steps of the controller for the simulation examples are reduced by fifty percent compared to the state-space method.