Distributed Fixed-Time Tracking and Containment Control for Second-Order Multi-Agent Systems: A Nonsingular Sliding-Mode Control Approach

This paper focuses on distributed fixed-time tracking consensus and containment control problems of second-order multi-agent systems (MASs) with directed topology. To make the offline design and convergence time estimation of the consensus protocol for second-order MASs possible, a novel nonsingular sliding-mode control method is established by introducing a time-varying scaling function in the design of the sliding surface. Subsequently, sufficient conditions ensuring fixed-time tracking consensus and containment control of the second-order MASs are obtained by using the proposed nonsingular sliding-mode control method. The results show that the estimated convergence time of considered MASs is independent of the initial values and other parameters of the system, where the convergence time on the sliding surface can be prescribed. Ultimately, two numerical examples are illustrated to verify the validity of the obtained results.