Practical adaptive time-varying output formation tracking for high-order nonlinear multi-agent systems using neural networks

Practical adaptive time-varying output formation tracking problems for high-order nonlinear strict-feedback multi-agent systems are investigated in this paper. The time-varying output formation tracking requires the followers' output vectors to track the output vector of the leader while achieving a time-varying formation. The dynamics of the leader and the followers can have uncertain mismatched nonlinearities while the leader's control input is also unknown. To deal with the mismatched nonlinearities, the backstepping techniques are utilized to construct the protocols. Firstly, visual controllers are designed to overcome the effects of the uncertainties while guaranteeing the stability of each layer. The complicated visual controllers are estimated by the neural networks. A full adaptive protocol is constructed with adaptive gains to avoid using the global information of the interaction topology. Then, an algorithm is presented to design the protocol, whose parameters are much less. Besides, the stability of the algorithm is proved by Lyapunov theories. Finally, simulation results are presented to prove the effectiveness.