Retrospective Cost Adaptive Control for Nonminimum-Phase Discrete-Time Systems, Part 1: The Ideal Controller and Error System

We present a direct adaptive controller for discrete-time (and thus sampled-data) systems that are possibly nonminimum phase. The adaptive control algorithm requires limited model information, specifically, knowledge of the first nonzero Markov parameter and the nonminimum-phase zeros (if any) of the transfer function from the control to the performance. This adaptive control algorithm is effective for stabilization as well as for command following and disturbance rejection, where the command and disturbance spectra are unknown. The novel aspect of this controller is the use of a retrospective performance, which is minimized using either an instantaneous or cumulative retrospective cost function.