Adaptive Stabilization of Uncertain Discrete-time Systems via Switching Control: The Method of Localization

In this chapter a new systematic switching control approach to adaptive stabilization of uncertain discrete-time systems with parametric uncertainty is presented. Our approach is based on a localization method which is conceptually diierent from supervisory adaptive control schemes and other existing switching adaptive schemes. Our approach allows for slow parameter drifting, infrequent large parameter jumps and unknown bound on exogenous disturbance. The unique feature of localization based switching adaptive control distinguishing it from conventional adaptive switching schemes is its rapid model falsiication capabilities. In the LTI case this is manifested in the ability of the switching controller to quickly converge to a suitable stabilizing controller. We believe that the approach presented in this chapter is the rst design of a switching controller which is applicable to a wide class of linear time invariant and time varying systems and which exhibits good transient performance. The performance of the proposed switching controllers is illustrated by many simulation examples.