Stabilization of systems with changing dynamics

Abstract

We present a framework for designing stable control schemes for systems whose dynamic equations change as they evolve on the state space. It is usually difficult or even impossible to design a single controller that would stabilize such a system. An appealing alternative are switching control schemes, where a different controller is employed on each of the regions defined by different dynamic characteristics and the stability of the overall system is ensured through appropriate switching scheme. We derive sufficient conditions for the stability of a switching control scheme' in a form that can be used for controller design. An important feature of the proposed framework is that although the overall hierarchy can be very complicated, the stability depends only on the immediate relation of each controller to its neighbors. This makes the application of our results particularly straight forward. The methodology is applied to stabilization of a shimmying wheel, where changes in the dynamics are due, to switches between sliding and rolling.