Fixed-Time and Predefined-Time Bipartite Consensus Tracking for Second-Order Multi-agent Systems Based on Sliding-Mode Approach

This study delves into fixed-time and predefined-time bipartite consensus tracking (BCT) of second-order multi-agent systems (MASs), where cooperative and competitive behaviors coexist, while accounting for bounded disturbances. Based on the sliding mode control method, the fixed-time and predefined-time control protocols are proposed to ensure the achievement of fixed-time and prescribed-time BCT for the MASs, which can effectively eliminate singularity and chattering. Leveraging Lyapunov stability, we establish a set of adequate conditions to achieve fixed-time and predefined-time BCT for second-order MASs. Furthermore, we present numerical simulation results to substantiate the theoretical conclusions.