Fixed-time nonsingular adaptive containment control for uncertain nonlinear multi-agent systems with predefined accuracy

This article studies the containment control problem for uncertain nonlinear multi-agent systems. To solve this problem, a performance-oriented fuzzy adaptive algorithm is proposed. By constructing a new Lyapunov function and using the predefined accuracy functions, the algorithm ensures the negative-definite property of the time derivative of the Lyapunov function while guaranteeing that the containment errors converge to a user-defined interval. Different from most existing results, the control algorithm proposed in this article realizes the negative-definite property of the time derivative of Lyapunov function without adjusting parameters. Then, an event-triggered mechanism is introduced to reduce the communication burden between the controller and the actuator. Moreover, by using the singularity-avoidance functions, a fixed-time fuzzy nonsingular controller is constructed to avoid the possible "singularity" problem in the backstepping recursive design. Based on the fixed-time stability criterion, it is proved that all output signals converge to a predefined interval in a fixed time. Finally, several simulation results further demonstrate the effectiveness of the presented control strategy.