Adaptive practical finite-time bipartite consensus of nonlinear multi-agent systems with input saturation and non-zero input leader

This paper investigates the practical finite-time bipartite consensus (PFBC) for a class of nonlinear multi-agent systems (MASs) with input saturation and non-zero input leader, where the leader’s input is unknown to all followers. Due to the existence of unknown control gain and input saturation in the system, it is impossible to directly compensate through the controller, which poses challenges to the design of control scheme. To deal with this situation, firstly, a smooth function is employed to approximate input saturation. Then, a new compensation function is designed to handle the impact of leader’s input. Afterwards, in order to ensure convergence speed and achieve PFBC, a new adaptive controller with a power exponential term is designed by combining compensation function and sign function. Compared with related works in this field, the scheme proposed in this paper can effectively reduce chattering while ensuring system performance. Finally, The simulation results have verified the effectiveness of the proposed PFBC control strategy.