Fixed-time Consensus Tracking Control of High-order Multi-agent Systems under Directed Graph

In this paper, the fixed-time consensus tracking problem is studied for a class of high-order multi-agent systems under directed graph. Firstly, the fixed-time terminal sliding mode surface is introduced such that if the sliding mode surface is reached, the fixed-time convergence of the local neighborhood errors can be guaranteed. Then, the virtual control law is proposed by using dynamic surface control technique at each step, and the actual control law is designed at the last step. According to the fixed-time stability theory, it is proved that the fixed-time tracking consensus will be achieved by applying the proposed approach. Finally, a simulation is conducted to clarify the effectiveness of the proposed control strategy.