Stabilization of Systems With Changing Dynamics

. 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 di#cult or even impossible to design a single controller that would stabilize such a system. An appealing alternative are switching control schemes, where a di#erent controller is employed on each of the regions defined by di#erent dynamic characteristics and the stability of the overall system is ensured through appropriate switching scheme. We derive su#cient 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..

Stabilization of systems with changing dynamics by means of switching

We present a framework for designing stable control schemes for systems whose dynamics change. The idea is to develop a controller for each of the regions defined by different dynamic characteristics and design a switching scheme that guarantees the stability of the overall system. We derive sufficient conditions for the stability of the switching scheme for systems evolving on a sequence of embedded manifolds. An important feature of the proposed framework is that if the conditions are satisfied by pairs of controllers adjacent in the hierarchy, the overall system will be stable. This makes the application of our results particularly straight forward. The methodology is applied to stabilization of a shimmying wheel, where changes in the dynamic behavior are due to switches between sliding and rolling