Practical time-varying output formation tracking for high-order nonlinear strict-feedback multi-agent systems with control gap using adaptive neural networks

Practical time-varying output formation tracking issues for high-order nonlinear strict-feedback multi-agent systems with control gap are studied in this paper. The outputs of the followers are desired to form a time-varying formation while tracking the leader’s output. Besides, the dynamics of each agent has high-order mismatched nonlinearities and control gap, and the leader has unknown control signal. Firstly, the mismatched nonlinearities, the control gap and the leader’s unknown control signal are transformed into the integrated uncertainties, and a practical time-varying output formation tracking protocol is constructed by using adaptive neural networks and back-stepping technique. Then, the procedures for designing the protocol are summarized to an algorithm including the feasible time-varying formation tracking condition and the criteria for the selection of the control parameters. Thirdly, the stability of the closed-loop multi-agent system can be guaranteed through the analysis method of the Lyapunov stability theory. Finally, a simulation example is presented for illustrating the effectiveness of the proposed method.