Retrospective cost model reference adaptive control for nonminimum-phase systems

This paper presents a direct model reference adaptive controller for single-input/single-output discrete-time (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 output. This controller uses a retrospective performance, which is a surrogate measure of the actual performance, and a cumulative retrospective cost function, which is minimized by a recursive-least-squares adaptation algorithm. This paper develops the retrospective cost model reference adaptive controller and analyzes its stability.