Retrospective cost adaptive control using concurrent controller optimization and target-model identification

Abstract

Retrospective cost adaptive control (RCAC) is a discrete-time adaptive control algorithm for stabilization, command following, and disturbance rejection. RCAC requires knowledge of the nonminimum-phase (NMP) zeros in the transfer function from the control input to the performance variable. This knowledge is embedded in the target model used to define the retrospective performance variable. Without this knowledge, RCAC has a tendency to cancel unmodeled NMP zeros. The contribution of the present paper is an extension of RCAC that alleviates the need to know the NMP zeros a priori. In particular, concurrent optimization is used to update the coefficients of the controller and target model, thus providing estimates of the unmodeled NMP zeros. Since the retrospective cost is a biquadratic function of these coefficients, an alternating convex search algorithm takes advantage of the closed-form minimizers of both quadratic cost functions. For comparison, the Matlab fminsearch routine is used to jointly optimize the controller and target model. These techniques are illustrated for SISO plants that are asymptotically stable, unstable, minimum phase, and nonminimum phase.