Leader–follower tracking in lipschitz nonlinear multi agent systems under undirected graph with noisy sinusoidal motion of the leader

A distributed control protocol is proposed in this paper for tracking a leader with a sinusoidal motion path considering an undirected communication graph. A multi-agent system (MAS) is considered in which the dynamics of all agents and the leader are nonlinear and contaminated with noise. Firstly, we assume that the states of the leader and all of the agents are measurable without noise. In this case, graph theory, Lyapunov approach and Lasalle principle are used to design a distributed control protocol for nonlinear MASs to follow the leader with nonlinear dynamics. Next, it is supposed that the leader has a sinusoidal motion and its neighbor followers observe the leader with noise. Therefore, the parameters of measured signal including amplitude, frequency and phase are unknown. In this way, a novel algorithm called Integral Linear Least Square (ILLS) is proposed to estimate unknown parameters of sinusoidal behavior of the leader which is contaminated by noise, accurately. Next, a distributed control algorithm is designed for multiagent systems with Lipschitz nonlinearities under undirected graph to track the estimated states of the leader with noisy sinusoidal motion. Finally, numerical simulations illustrate the effectiveness of the proposed algorithms.