Fixed-time consensus of second-order multi-agent systems with nonlinear dynamics

The authors mainly discuss finite-time tracking consensus and fixed-time tracking consensus of multi-agent systems for second-order with inherent nonlinear function and disturbance under a directed interaction graph in this work. By sliding mode control theory, consensus tracking controllers are proposed to ensure that sliding mode can be reached and maintain on it in finite time and fixed time. By using some theoretical knowledge of control, such as graph theory and Lyapunov theory, we make the system to reach consensus in finite time and fixed time by choosing the right parameters. In addition, the calculation leads to the conclusion that settling time of finite-time consensus is associated to initial state, while settling time of fixed-time consensus is interrelated to parameters but not to the initial state. The feasibility of the theory is proved by simulation experiments.