Time‐varying formation control for multi‐agent systems under directed topology base on gain re‐adaptation fault‐tolerant compensation approach

Abstract The distributed fault‐tolerant time‐varying formation control problem for second‐order multi‐agent systems (MAS) with loss‐of‐effectiveness and bias actuator faults over the directed topology is investigated in this article. A novel robust fault‐tolerant state feedback controller is constructed with the re‐adaptation gain and adaptive compensation, where the re‐adaptation control gain is introduced to accomplish formation control with no need for any global knowledge of interaction network among the agents in the entire system. The adaptive compensation is addressed to cope with the unknown bound of faults and time‐varying formation. Moreover, the adaptive laws will not always rise because of the influence of measurement noise. On the analysis of Lyapunov stability, one can obtain that all signals of the closed‐loop fault‐tolerant control system are uniformly bounded, and the formation errors can asymptotically converge to zero. The numerical simulation of second‐order MAS is performed to prove the effectiveness of the mentioned results.