Frequency-domain stability analysis of retrospective-cost adaptive control for systems with unknown nonminimum-phase zeros

We develop a multi-input, multi-output direct adaptive controller for discrete-time, possibly nonminimum-phase, systems with unknown nonminimum-phase zeros. The adaptive controller requires limited modeling information about the system, specifically, Markov parameters from the control input to the performance variables. Often, only a single Markov parameter is required, even in the nonminimum-phase case. We analysis the stability of the algorithm using a time-and-frequency-domain approach. We demonstrate the algorithm on disturbance-rejection problems, where the disturbance spectra are unknown. This controller is based on a retrospective performance objective, where the controller is updated using either batch or recursive least squares.