Distributed finite-time configuration containment control for satellite formation

Abstract

This paper investigates the distributed finite-time configuration containment control problem for satellite formation with multiple leader satellites under directed communication topology. We consider that only a portion of follower satellites can receive leaders’ information and unknown perturbations and model uncertainties exist in the dynamics models of satellites. By defining the relative configuration error functions and selecting suitable nonsingular terminal sliding mode variables, a fully distributed finite-time configuration containment control scheme is proposed using the matrix properties of graph theory. The Lyapunov method is used to demonstrate the finite-time convergence property of the closed-loop systems. Numerical examples and comparisons with other methods are provided to show the effectiveness and the performance of the proposed control strategy.

Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

“…In MASs, in order to accomplish the assigned tasks, the agents communicate with each other in a certain way. Compared with a single agent, MASs possess advantages of more flexibility, stronger survivability, and lower cost so that they are widely used in formation flying spacecraft, multirobot systems, and multiple mechanical systems …”

“…Euler‐Lagrange (EL) equations can describe the systems with nonlinear dynamic characteristics. Thus, they are widely used in nonlinear MAS modeling . The MASs described by EL equations can be named as multiple EL systems.…”

“…For centralized control, the control signals of all the agents are sent by humans or one specific agent in the systems. Compared with centralized control schemes, distributed control methods possess higher flexibility and adaptability so as to be widely adopted in engineering situations . For distributed control methods, communication topology is used to describe the communication relationships among agents.…”

“…It was demonstrated by Lyapunov method that all the followers could converge to the convex hull spanned by the leaders in finite time. Selecting an appropriate nonsingular terminal sliding mode, Sun et al put forward a distributed finite‐time configuration containment control law for satellite formation with multiple leaders. The finite‐time convergence property of the systems was demonstrated and the singularity was avoided effectively.…”

“…Compared with centralized control schemes, distributed control methods possess higher flexibility and adaptability so as to be widely adopted in engineering situations. 1,3 For distributed control methods, communication topology is used to describe the communication relationships among agents. It can be classified into two classes, which are undirected topology 5,12 and directed topology.…”