Stabilization of Systems with Changing Dynamics

We present a framework for designing stable control schemes for systems with changing dynamics – systems whose dynamics change as the state evolves through different regions in the state space. Systems with changing dynamics (SCD) 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. With partial order, the study of the stability of the system is reduced to the study of relationships among the immediate neighbors in the partial order. This significantly simplifies the analysis and design processes. The methodology is applied to stabilization (of a relative equilibrium) of a two-wheel mobile robot of the Hilare type, where the wheels are allowed to slip. The example demonstrates that the approach is easy to use and that the partial order concept naturally leads to modularity in the controller design.