Fixed-time sliding mode consensus tracking for second-order nonlinear multi-agent system with persistent dwell-time switching topologies

This article investigates the problem of fixed-time sliding mode consensus tracking for nonlinear second-order multi-agent system, in the presence of disturbances and actuator attacks. The interaction topology graph of multi-agent system is directed and switched, and the switching topologies satisfy a more general persistent dwell-time switching mechanism. To account for the disturbances, actuator attack, and switching topologies, a nonsingular sliding mode control law with distributed switching scheme is constructed to guarantee the fixed-time reachability to a sliding surface. By using multiple Lyapunov functions, some new sufficient criteria are derived for fixed-time consensus tracking of the multi-agent system with persistent dwell-time switching topologies. To illustrate the proposed approach, we present a numerical example and a physical example of the single pendulum model.