Adaptive Control Based on Retrospective Cost Optimization.

Abstract

This dissertation studies adaptive control of multi-input, multi-output, linear, time-invariant, discrete-time systems that are possibly unstable and nonminimum phase. We consider both gradient-based adaptive control as well as retrospective-cost-based adaptive control. Retrospective cost optimization is a measure of performance at the current time based on a past window of data and without assumptions about the command or disturbance signals. In particular, retrospective cost optimization acts as an inner loop to the adaptive control algorithm by modifying the performance variables based on the difference between the actual past control inputs and the recomputed past control inputs based on the current control law. We develop adaptive control algorithms that are effective for systems that are nonminimum phase.

We consider discrete-time adaptive control since these control laws can be implemented directly in embedded code without requiring an intermediate discretization step. Furthermore, the adaptive controllers in this dissertation are developed under minimal modeling assumptions. In particular, the adaptive controllers require knowledge of the sign of the high-frequency gain and a sufficient number of Markov parameters to approximate the nonminimum-phase zeros (if any). No additional modeling information is necessary.

The adaptive controllers presented in this dissertation are developed for full-state-feedback stabilization, static-output-feedback stabilization, as well as dynamic compensation for stabilization, command following, disturbance rejection, and model reference adaptive control. Lyapunov-based stability and convergence proofs are provided for special cases. We present numerical examples to illustrate the algorithms' effectiveness in handling systems that are unstable and/or nonminimum phase and to provide insight into the modeling information required for controller implementation.