Finite-Time Bipartite Tracking Control for Double-Integrator Networked Systems With Cooperative and Antagonistic Interactions

This paper is concerned with bipartite tracking for double-integrator networked systems with signed communication graphs, where both cooperative and antagonistic interactions coexist. A finite-time bipartite tracking framework is established, where followers track either the state or the opposite state of a leader. Different from some conventional results with convergence over an infinite time horizon, the finite-time convergence in this paper is achieved in an accurate manner. Under structurally balanced signed graphs, an integral sliding mode based finite-time bipartite tracking controller is proposed. The construction of an integral sliding mode variable is to ensure that the system dynamics is driven onto a sliding surface in finite-time. On the sliding surface, neighbouring states are used together with the homogeneous technique to guarantee that bipartite tracking is achieved in finite-time. To further realize fixed-time bipartite tracking, a controller is designed by using the integral sliding mode and the bi-limit homogeneous concept. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed controllers.