Fixed-time output consensus for nonlinear heterogeneous multi-agent systems with disturbances

The fixed-time output consensus is considered in this article for heterogeneous nonlinear first-order and second-order multi-agent systems with disturbances. Firstly, we design a distributed observer by the fixed-time consensus theory, realizing distributed control of the system under directed graph. Secondly, designing a fixed-time controller for the first-order nonlinear system with disturbances by using constant exponential and time varying exponential coefficient methods. For the second-order nonlinear system with both matched and mismatched disturbances, designing a fixed-time tracking controller by using the backstepping method and robust sliding mode control. The designed controller effectively suppresses the mismatched disturbance of system and makes the multi-agent system achieve output consensus in a fixed time. Finally, we demonstrate the effectiveness of the protocol through numerical examples.