Date of Award

Spring 1975

Document Type


Degree Name

Doctor of Engineering Science in Electrical Engineering


Electrical Engineering

First Advisor

Marshall Chuan Yung Kuo

Second Advisor

Murray Lieb

Third Advisor

Joseph J. Padalino

Fourth Advisor

Harlan J. Perlis


This dissertation deals with linear systems subjected to stochastic disturbances. The class of stochastic processes considered is the class of second order stochastic processes characterized by having finite continuous covariance. The properties of the covariance provide means to formulate optimization problems without the difficulties present when the covariance is not finite or continuous.

The first aspect studied was several classes of optimal control problems. The effects of the stochastic processes were approximated by the effects of its first two moments. This procedure resulted in allowing optimal system controls to be found whatever the first two moments of the stochastic input were, or "worst case" optimal controls were found. Differential game theory was used to solve the "worst case" problem.

Then, a model reference adaptive control system was employed to permit simultaneous parameter identification and control to be obtained in an on-line environment. The parameter identification was accomplished using gradient or steepest descent techniques. The control inputs were updated as the parameters were changed yielding sub-optimal control of the physical system. In addition, minimum error covariance estimation of linear systems with second order stochastic disturbances was developed.