Fault-tolerant formation control of stochastic nonlinear multi-agent systems with time-varying weighted topology

In this paper, the fault-tolerant formation control of nonlinear stochastic multi-agent systems in the presence of actuator faults, disturbances, and time-varying weighted topology is considered. While most traditional fault-tolerant control methods in the literature use fixed weights on the topology edges, in this study these weights are considered time-varying using a pre-designed function, which allows formulating the system more realistically. Moreover, in contrast with previous works on fault-tolerant multi-agent systems, in this study, the model of the agents is considered to be stochastic in general. Furthermore, the actuators of the agents are considered to have a time-varying fault of additive and multiplicative types. A passive and an active fault-tolerant controllers are designed based on the back-stepping sliding-mode approach. In the passive method, a constant robust controller is proposed using an upper bound of the faults while, in the active controller, the additive and multiplicative faults are estimated using adaptive laws. The active and passive fault-tolerant controllers guarantee that the formation errors converge to a bounded region near the origin in a mean-square sense and all of the existing signals in the closed-loop system remain bounded in probability. The results of the formation control are extended to consensus control as well. Finally, a stochastic multi-aircraft model and an RLC circuit with stochastic part are used as two case studies to illustrate the effectiveness of the proposed design method.