Practical fixed-time bipartite consensus control for nonlinear multi-agent systems: A barrier Lyapunov function-based approach

Abstract

This paper develops a practical fixed-time bipartite consensus control framework for the uncertain nonlinear multi-agent systems (MASs) via using a barrier Lyapunov function (BLF)-based approach. Distinguish from the most existing results, the unknown nonlinearities of MASs in this paper are tackled by utilizing the robustness of BLF instead of applying fuzzy logic systems/neural networks approximating. In order to avoid feasibility verification in the traditional BLF method, a piecewise and differentiable function named the shift function is skillfully inserted into the coordination transformation of the controller design process, allowing not only the initial value of MASs states to be chosen arbitrarily, but also the settling time of bipartite consensus errors can be pre-designated. According to the backstepping framework, an approximated-free control algorithm is developed by combining the shift function with BLF, which guarantees that for any initial state of MASs, the outputs of all the agents can achieve the practical fixed-time bipartite consensus tracking, and all the signals in closed-loop systems are bounded. Especially, the settling time and the tracking error accuracy can be appointed by the designer. Finally, simulation results are given to show the effectiveness of the proposed control method.