Adaptive containment control for a class of multi-agent systems with unknown actuator failures

In this paper, an adaptive containment control scheme is proposed for a class of high-order nonlinear multi-agent systems with unknown actuator failures. With the aid of a matrix factorization, only the signs of leading principal minors of the control gain matrices need to be known. A two-step design method fusing the ideas of sliding mode control and backstepping control is developed to construct the controllers, and a similarity transformation and a bound estimation approach are introduced to handle the actuator failures. The proposed scheme allows the total number of failures to be infinite and is able to guarantee global stability of the overall closed-loop system. Moreover, it is proved that the containment errors can converge to an arbitrarily small residue set. Simulation results are presented to illustrate the effectiveness of the proposed scheme.