Finite-time Optimal Formation Control for Linear Multi-agent Systems

This paper investigates the problem of finite-time formation control for multi-agent systems with general linear dynamics. First, the formation problem considered is converted into the motion planning problem. Then, by using Pontryagins maximum principle (PMP), an optimal formation control law is developed for multi-agent systems which satisfy some invertible conditions. With this control law, the multi-agent systems achieve the desired formation in finite time, where the formation configurations and the settling time are specified in advance according to task requirements. Meanwhile, a performance index is guaranteed to be optimal. Further, it is proved that the conditions concerned are invertible if and only if the linear systems we considered are controllable.