Multi-vehicle coordinated motion via stabilization of time-varying sets

In this paper, we develop stability and control framework for time-varying sets of nonlinear time-varying dynamical systems. Furthermore, we apply the developed control framework to the problem of multi-vehicle coordinated motion to design distributed controllers for individual vehicles moving in a specified formation. The main idea of our approach is that a moving formation of vehicles can be characterized by a time-varying set in the state space, and hence, the problem of distributed control design for multi-vehicle coordinated motion is equivalent to design of stabilizing controllers for time-varying sets of nonlinear dynamical systems. The control framework is shown to ensure global exponential stabilization of multi-vehicle formations.