Adaptive control within the class of stabilizing controllers for a time-varying nominal plant†

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Abstract
In this paper, we consider enhancing the performance of a stabilizing causal controller K0 (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, K 0. 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.

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