Simplified optimized finite-time containment control for a class of multi-agent systems with actuator faults

In this paper, for a class of multi-agent systems with unknown dynamic functions and unknown actuator faults, the optimized finite-time containment control problem based on optimized backstepping technology is investigated. The optimal control strategy is obtained through a simplified reinforcement learning algorithm with the structure of identifier-critic-actor. Based on such a structure, the identifier, the critic and the actor are applied to estimate unknown dynamic functions, evaluate system performance and implement control behavior, respectively. The updating laws of the actor and critic are derived based on the gradient descent method of a simple positive function rather than the square of Bellman residual, which makes the updating laws simpler and eliminates the harsh persistent excitation condition. In addition, in order to eliminate the effect of actuator faults on system stability, a network-based fault observer is constructed to observe online actuator faults. Furthermore, the designed finite-time optimal distributed containment controllers ensure that the followers can ultimately converge to the convex hull composed by leaders within a predetermined finite time. Finally, a numerical simulation result and a practical example are presented to verify the effectiveness of the proposed control method.