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

Abstract

SummaryThis 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.