Stability of a Reduced Order Model Reference Adaptive Control System with Persistent Excitation.

摘要

This thesis contains two major results, as well as illustrative simulation examples. The first major result is that for a certain class of inputs there exists a unique equilibrium for a model reference adaptive system when the nomial plant is perturbed by a high frequency unmodelled dynamics. The second major result is that, for a small enough perturbation, this equilibrium is exponentially stable. Chapter 2 provides a transfer function description of the system and contains a section showing that a small singular perturbation has a small effect on the equilibrium values of the adjustable gains. In Chapter 3, several results were derived including the second major result of the thesis. The chapter begins with definitions and theorems to be used in the derivations in the rest of the chapter. Then the differential equations describing the system are presented and an error system is derived. In Chapter 4, two simple examples are pesented which show that the system indeed remains exponentially stable when high frequency unmodelled dynamics perturb the original system. The examples also show that estimates of the range of stable perturbations based upon the proof of Theorem 3.9 are so conservative that these estimates are not of practical use. In Chapter 5, offers some concluding remarks and suggestions for future research.