Practical time-varying formation tracking control for second-order nonlinear multi-agent systems based on the distributed extend state observer

Abstract

Practical time-varying formation tracking analysis and design problems for second-order nonlinear multi-agent systems are investigated by using a novel distributed extended state observer, where the formation tracking error can be arbitrarily small. Different from the previous work on formation tracking problems, the states of followers form a predefined time-varying formation while tracking the state of the leader with unknown but derivative-bounded control input. Besides, the dynamics of each agent has heterogeneous nonlinearity. Firstly, a novel distributed extended state observer is constructed by using only neighboring relative information, which can process not only the heterogeneous nonlinearity of each follower, but also the unknown control input of the leader. Secondly, a practical time-varying formation tracking control protocol with the distributed extended state observer is proposed. Additionally, the stability of the closed-loop multi-agent system under the protocol is proven by using the Lyapunov theory. Thirdly, an approach is derived to design the control parameters in the practical time-varying formation tracking protocol by solving a linear matrix inequality. Finally, simulation results are given to illustrate the effectiveness of the obtained theoretical results.