Prescribed-Time Tracking Consensus for Second-Order Nonlinear Multi-agent Systems via Sliding Mode Control Under Directed Topology

The focus of this paper is to address the challenge of achieving prescribed-time tracking consensus control for second-order multi-agent systems (MASs) with directed topology. To drive the system state to the prescribed sliding surface and enhance the system’s robustness against disturbances, a novel sliding mode control (SMC) strategy is proposed. This approach introduces a dynamically changing scaling function as part of the sliding surface design, effectively addressing disturbances and accounting for the system’s nonlinear characteristics. By employing the newly proposed SMC strategy, sufficient conditions are derived to guarantee the prescribed-time tracking consensus for second-order MASs. The findings reveal that the prescribed-time convergence is insensitive to the initial values of the system and other system parameters. Furthermore, the approach demonstrates robustness and allows for manual setting of the convergence time. Finally, the effectiveness of this method is verified through a numerical simulation example.