Extensions of Retrospective Cost Adaptive Control: Nonsquare Plants, and Robustness Modifications.

Abstract

Controllers that have adjustable parameters, and an update law for adjusting these parameters, are called ``adaptive controllers''. Adaptive controllers typically entail assumptions about the dynamic order, relative degree or transmission zeros of the system, and may not be applicable to systems that are not positive real, passive, or minimum phase. In 1980s, the fragility of adaptive controllers to violations in these assumptions has been demonstrated through various counterexamples. This motivated the development of robustness modifications for adaptive controllers, which is the main goal of this dissertation.

In this dissertation, we focus on retrospective cost adaptive control (RCAC), which is a direct, digital adaptive control algorithm. RCAC is applicable to MIMO, nonminimum-phase (NMP) systems, but it assumes that the NMP zeros of the plant, if any, are known.

The main contribution of this work includes theory and analysis for retrospective cost adaptive control of nonsquare systems and development of a modified, robust RCAC update law for maintaining stability and convergence in the presence of unmodeled NMP zeros.