Adaptive Control within the Class of Stabilizing Controllers for a Time Varying Nominal Plant

Abstract

In this paper, we consider enhancing the performance of a stabilizing causal controller Ko (possibly time varying) for a causal nominal plant G (possibly time varying), with controller augmentations including an adaptive stable subsystem Q. The objective is to search on-line in the class of stabilizing causal controllers for the nominal plant, characterized in terms of Q and state space descriptions of G, Ko. For the case of time-invariant plants, most of the algorithms and theory of the paper specialize to known results. One formulation of the coprime factorizations using state- space description of time-varying systems, and associated characterization of the class of all stabilizing causal controllers used in our work, specializes to known results when the stabilizing controller has a full order state estimate feedback state space description.So as to view the results in terms of familiar schemes, specialization to the well-studied self-tuning regulator and parallel model reference adaptive controller are presented. The latter provides an illustration of the application of the results to two-degree-of-freedom design.