## LSU Historical Dissertations and Theses

1995

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Electrical and Computer Engineering

Guoxiang Gu

#### Abstract

This dissertation addresses the problem of unifying identification and control in the paradigm of ${\cal H}\sb\infty$ to achieve robust adaptive control. To achieve robust adaptive control, we employ the same approach used for identification in ${\cal H}\sb\infty$ and robust control in ${\cal H}\sb\infty.$ In the modeling part, we aim not only to identify the nominal plant, but also to quantify the modeling error in ${\cal H}\sb\infty$ norm. The linear algorithm based on least-squares is used, and the upper bounds for the corresponding modeling error are derived. In the control part, we aim to achieve the performance specification in frequency domain using innovative model reference control. New algorithms are derived that minimize an ${\cal H}\sb\infty$ index function associated with the deviation between the performance of the feedback system to be designed, and that of the reference model. The results for the modeling and control part are then combined and applied to adaptive control. It is shown that with mild assumption on persistent excitation, the least squares algorithm in frequency domain is equivalent to the recursive least squares algorithm in time domain. Moreover, finite horizon ${\cal H}\sb\infty$ is employed to design feedback controller recursively using the identified model that is time varying in nature. The robust stability of the adaptive feedback system is then established.

178

COinS