Retrospective Cost Adaptive Control for Nonminimum-Phase Systems with Uncertain Nonminimum-Phase Zeros Using Convex Optimization

Retrospective cost adaptive control (RCAC) can be applied to command following and disturbance rejection problems with plants that are possibly MIMO, unstable, and nonminimum phase. RCAC requires knowledge of a bound on the first nonzero Markov parameter as well as knowledge of the nonminimum-phase zeros of the plant, if any. The goal of the present paper is to increase the robustness of RCAC to uncertainty in the locations of the nonminimum-phase zeros. Specifically, a convex constraint is imposed on the poles of the controller in order to prevent the adaptive controller from attempting to cancel the nonminimum-phase zeros. Numerical results show that, when constrained convex optimization is used at each step, the transient response is improved and the adaptive controller has increased robustness to uncertainty in the locations of the nonminimum-phase zeros.