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.