Direct adaptive command following and disturbance rejection for minimum phase systems with unknown relative degree

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.