Design of switching controllers for systems with changing dynamics

Abstract

We present a framework for designing stable control schemes for systems with changing dynamics (SCD). Such systems form a subset of hybrid systems; their stabilization is therefore a problem in hybrid control. It is often difficult or even impossible to design a single controller that would stabilize a SCD. An appealing alternative are switching control schemes, where a different controller is employed in each dynamic regime and the stability of the overall system is ensured through an appropriate switching scheme. We formulate a set of sufficient conditions for the stability of a switching control scheme. We show that by imposing a hierarchy among the controllers, sufficient conditions can be formulated in a form suitable for the controller design. The hierarchy is formally defined through a partial order. Our methodology is applied to stabilization of a two-wheel mobile robot of the Hilare type, where the wheels are allowed to slip.