Practical Explicit-time Stabilization of Multi-agent Control Systems with Proportional Feedback Design

The more complex nonlinear feedback in the design of controller for multi-agent systems (MASs), the more chattering is likely to occur in the control input. However, it is difficult for the existing methods to achieve fixed-time control only through linear proportional feedback. For solving this problem, a novel explicit-time proportional control method is proposed for MASs. It can achieve the practical conditionally fixed-time stability of system. Firstly, a practical conditionally fixed-time stable system is proposed by a special proportional function. Then, a nominal controller is designed based on this stability system, which is called as practical explicit-time stabilization. In the end, the proposed method is applied to MASs, which makes this control system error converge to a predefined neighborhood of zero within an explicit time. Compared with the existing predefined-time back-stepping control methods, the smoothness of control input is improved by solving the problems of singularity and high gain. Theoretical analysis and simulation verify the main results.