A Computational Study of the Performance and Robustness Properties of Retrospective Cost Adaptive Control

Abstract

We present a computational study of a discrete-time adaptive control algorithm that is effective for multi-input, multi-output systems that are either minimum phase or nonminimum phase. The adaptive control algorithm requires limited model information, specifically, the first nonzero Markov parameter and the nonminimum-phase transmission zeros of the transfer function from the control signal to the performance measurement. Furthermore, the adaptive control algorithm is effective for stabilization, command following, and disturbance rejection. For command following and disturbance rejection, the algorithm does not require knowledge of the command or disturbance spectrum. We explore computationally the algorithm's performance and robustness in the presence of errors in the required modeling information.

Retrospective Cost Model Reference Adaptive Control for Nonminimum-Phase Systems

“…While the analysis presented herein relies on Assumptions 2 and 3, numerical examples demonstrate that RC-MRAC is robust to errors in the model information assumed by Assumptions 2 and 3. More specifically, the numerical examples presented [20,25] suggest that Assumption 2 may be able to be weakened to the assumption that the sign of d is known and an upper bound on the magnitude of d is known. Furthermore, the current paper presents numerical examples that show that RC-MRAC is robust to errors in the nonminimumphase zero estimates.…”

“…Furthermore, the current paper presents numerical examples that show that RC-MRAC is robust to errors in the nonminimumphase zero estimates. Additional numerical examples are presented in [25].…”

“…Therefore, it follows from Eqs. (18)(19)(20)(21)(22)(23)(24) and (27) that, for all k n c , the ideal closed-loop system (25) and (26), has the (2n c 1)th order nonminimal-state-space realization…”

“…Then there exists an ideal fixed-gain controller (26) of order n c such that the following statements hold for the ideal closed-loop system consisting of Eqs. (25) and (26), which has the (2n c 1)th-order nonminimal-state-space realization (28-30): 1) For all initial conditions ;0 and for all k k 0 ≜ 2n c n u d,…”

“…Techniques developed to prevent pole-zero cancellation for indirect adaptive control [27] may have application to this problem. Nevertheless, numerical examples suggest that asymptotic unstable pole-zero cancellation does not occur [20,21,25]. Note that the leading coefficient of m q is chosen such that the reference model has unity gain at z 1.…”