This paper considers parameter-monotonic direct adaptive command following and disturbance rejection for single-input single-output minimum-phase linear time-invariant systems with knowledge of the sign of the high-frequency gain (first non-zero Markov parameter) and an upper bound on the magnitude of the high-frequency gain. We assume that the command and disturbance signals are generated by a linear system with known characteristic polynomial. Furthermore, we assume that the command signal is measured, but the disturbance signal is unmeasured. The first part of the paper is devoted to a fixed-gain analysis of a high-gain-stabilizing dynamic compensator for command following and disturbance rejection. The compensator utilizes a Fibonacci series construction to control systems with unknown-but-bounded relative degree. We then introduce a parameter-monotonic adaptive law and guarantee asymptotic command following and disturbance rejection.

We present a direct adaptive controller for discrete-time (and thus sampled-data) systems that are possibly nonminimum phase. The adaptive control algorithm requires limited model information, specifically, knowledge of the first nonzero Markov parameter and the nonminimum-phase zeros (if any) of the transfer function from the control to the performance. This adaptive control algorithm is effective for stabilization as well as for command following and disturbance rejection, where the command and disturbance spectra are unknown. The novel aspect of this controller is the use of a retrospective performance, which is minimized using either an instantaneous or cumulative retrospective cost function.

No abstract

This paper presents a direct model reference adaptive controller for single-input/single-output discrete-time (and thus sampled-data) systems that are possibly nonminimum phase. The adaptive control algorithm requires knowledge of the nonminimum-phase zeros of the transfer function from the control to the output. This controller uses a retrospective performance, which is a surrogate measure of the actual performance, and a cumulative retrospective cost function, which is minimized by a recursive-least-squares adaptation algorithm. This paper develops the retrospective cost model reference adaptive controller and analyzes its stability.

No abstract