## LSU Historical Dissertations and Theses

#### Title

Multiobjective Optimal Filtering and Control.

1998

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Electrical and Computer Engineering

Kemin Zhou

#### Abstract

A fundamental question in feedback control design is how to achieve desired performance under system uncertainties and external disturbances. The well-known LQG and ${\cal H}\sb2$ control design techniques are well suited for achieving some well-defined optimal transient performance under certain classes of stochastic external disturbances such as white noise. However, these optimal control design techniques are highly model dependent and may be very sensitive to parameter variations and system uncertainties. The ${\cal H}\sb{\infty}$ control theory, on the other hand, was developed precisely because of the desire to overcome these deficiencies. One potential shortfall of the existing ${\cal H}\sb{\infty}$ control design method is that it is very hard to handle transient performance naturally. Thus it is desirable to develop a systematic design technique that combines the good aspects of both LQG (or ${\cal H}\sb2$) and ${\cal H}\sb{\infty}$ design techniques. This is precisely the motivation for the multiobjective design framework developed in this dissertation. Motivated by the development of a time domain game approach for ${\cal H}\sb2$/${\cal H}\sb{\infty}$ control, three multiobjective design problems related to filtering and control are formulated on time domain in this dissertation. Based on a new constrained optimization result proved in this dissertation and ${\cal H}\sb{\infty}$ control design, the multiobjective filtering problem has been solved by an optimally designed filter while the multiobjective control problems have been solved by combining an optimally designed filter and a feedback gain. It is shown that all the results can be obtained by solving the corresponding set of coupled Riccati equations.

9780591997675

94

COinS