Distributed observer-based time-varying formation tracking for high-order multi-agent systems with nonlinear dynamics

Time-varying formation tracking problems for high-order nonlinear multi-agent systems are investigated by using a distributed observer-based method. Different from the previous work, the states of followers form a predefined time-varying formation while tracking the states of the leader with unknown but bounded control input. Besides, the dynamics of each agent is high-order and has nonlinearity. Firstly, a nonlinear time-varying formation tracking control protocol is proposed based on the distributed observer which is constructed using only local neighboring output information. Secondly, an algorithm with three steps is proposed to design the distributed observer-based formation tracking protocol, where the time-varying formation tracking feasibility condition is given. Thirdly, by using Lyapunov theory, the stability of the proposed algorithm is proven. Finally, a numerical example with three followers and one leader is provided to demonstrate the effectiveness of the obtained results.