Retrospective cost model reference adaptive control for nonminimum-phase discrete-time systems, Part 1: The adaptive controller

We present a direct model reference adaptive controller for discrete-time systems (and thus sampled-data systems) that are possibly nonminimum-phase. The adaptive control algorithm requires knowledge of the nonminimum phase zeros of the transfer function from the control to the tracking error. This paper and its companion paper (Part 2) together analyze the stability of the instantaneous (gradient-based) retrospective cost model reference adaptive controller and the cumulative (recursive-least-squares-based) retrospective cost model reference adaptive controller. Part 1 develops the adaptive controllers and proves the existence of an ideal control law. Part 2 presents the closed-loop error system and provides a closed-loop stability analysis.