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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. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive second-order sliding mode (SOSM) control method is proposed by combining a new adaptive strategy with the backstepping-like technique. The new adaptive strategy is first constructed by means of the equivalent control for which a sliding-mode-based filter is employed rather than the widely-used low-pass filter such that the parameter restriction under the usage of low-pass filter can be relaxed. Then, by applying the proposed adaptive strategy and the idea of adding a power integrator, an adaptive SOSM method is established to finite-time stabilize the sliding variables. The feature of the proposed SOSM method lies in that the gain will vary with the size of the lumped uncertainty so as to avoid the overestimation of the gain. The stability analysis is given based on the finite-time Lyapunov theory. The theoretical results are finally applied to the voltage regulation problem of a Buck converter. [ABSTRACT FROM AUTHOR]