Localization based switching adaptive controllers

Many different types of adaptive or universal controllers", capable of dealing with a very broad range of linear time-invariant systems, have been proposed. One class of such controllers uses switching between a finite, or at least countable, number of fixed controllers until stability is detected. Such controllers are very attractive from a theoretical viewpoint, in providing stabilization and asymptotic performance for a broad class of plants. However, such controllers are also known to have very poor transient properties, due to the long time required to search for a stabilizing feedback. The key contribution of this paper is to introduce the "method of localization" which can greatly improve the speed of the search. The method is described for linear time-invariant discrete time systems of known nominal order, with disturbances and noise present. Analysis and simulations demonstrate the potential for greatly improved transient performance.