Distributed time-varying formation control for second-order nonlinear multi-agent systems based on observers

Abstract

In this paper, time-varying formation analysis and design problems for second-order nonlinear multi-agent systems are studied using a distributed observer-based method. The formation in this paper can be specified by time-varying continuously differentiable vectors and the dynamics of each agent has nonlinearity. Firstly, a nonlinear time-varying formation control protocol is proposed based on the distributed observer. Then a nonsingular transformation matrix is constructed using the property of the Laplacian matrix. Sufficient conditions for the second-order nonlinear multi-agent systems to achieve time-varying formations are presented using only position feedback, where a description of the feasible time-varying formation set is given. Thirdly, an algorithm with three steps is proposed to design the distributed observer-based formation control protocol. By using the Lyapunov theory, the stability of the proposed algorithm is proven. Finally, a numerical example with five nonlinear agents is provided to demonstrate the effectiveness of the obtained results.