Distributed adaptive practical time-varying tracking control for second-order nonlinear multi-agent system using neural networks

Abstract

Practical adaptive time-varying formation tracking problems for second-order nonlinear multi-agent systems are investigated using neural networks, where the time-varying formation tracking error can be arbitrarily small. Different from the previous work, the states of followers form a predefined time-varying formation while tracking the states of the leader with unknown control input. Besides, the dynamics of each agent has heterogeneous nonlinearity. Firstly, for the case where the control input of the leader is unknown, a nonlinear practical time-varying formation tracking protocol using adaptive neural networks is proposed which is constructed using only local neighboring information. Secondly, sufficient conditions for the second-order nonlinear multi-agent systems to achieve practical time-varying formation are presented, where a novel practical time-varying formation tracking feasibility condition is given. Thirdly, an approach is presented to design the control parameters for distributed practical formation tracking control protocol. The stability of the closed-loop system is proven by using the Lyapunov stability theory. Finally, simulation results are given to illustrate the effectiveness of the obtained results.