Fixed-time consensus tracking control of second-order multi-agent systems with inherent nonlinear dynamics via output feedback

This paper is devoted to the fixed-time consensus tracking control problem for a class of second-order nonlinear multi-agent systems. Firstly, a fixed-time consensus control protocol with full state feedback is proposed, which is consisted of three parts: the higher-order components for uniformly bounded convergence for any initial states, the lower-order components for exact finite time convergence to zero and the linear components for dominating the nonlinear terms in the system dynamics, respectively. By using the Lyapunov approach and bi-limit homogeneous theory, it can be proved that under the designed control protocol the fixed-time consensus tracking control can be achieved. To overcome the lack of the velocity measurements, a fixed-time convergent state observer is designed to estimate the velocity information for each agent. Then a new observer-based fixed-time output feedback control protocol is designed, which can guarantee that the states of all agents can converge to that of the leader in a fixed time. Finally, numerical simulations are performed to demonstrate the fixed-time performance of the proposed control protocol and observer.