This paper investigates the fault-tolerant time-varying formation control problems for high-order linear multi-agent systems in the presence of actuator failures. Firstly, a fully distributed formation control protocol is presented to compensate for the influences of both bias fault and loss of effectiveness fault. Using the adaptive online updating strategies, no global knowledge about the communication topology is required and the bounds of actuator failures can be unknown. Then an algorithm is proposed to determine the control parameters of the fault-tolerant formation protocol, where the time-varying formation feasible conditions and an approach to expand the feasible formation set are given. Furthermore, the stability of the proposed algorithm is proven based on the Lyapunov-like theory. Finally, two simulation examples are given to demonstrate the effectiveness of the theoretical results.
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