UH Catalog Data: Cr.3 (3-0)

Prerequisite: ECE 6325 (or 5335) or consent of instructor.

Synthesis of optimal stationary and time-varying linear control systems
based upon random signal characteristics and statistical performance criteria.
Adaptive control systems.

Instructor's Suggestions:
Basic concepts of probability and statistics (such as mean, (co)variance,
and least-squares principle) are necessary and basic knowledge on discrete
Gaussian random sequences is preferable.

Textbook (required):
G. Chen, Goong Chen and S. H. Hsu: Linear Stochastic Control Systems,
CRC Press, 1995. Only Part II (Chapters 4,5,6) of the book will be covered
in detail. The rest of the text will be used as reference material.

Reference (recommended):
C. K. Chui and G. Chen: Linear Systems and Optimal Control, Springer-Verlag,
1989.

General Description:

Optimal filtering, identification, control and adaptive control of discrete-time
linear systems will be studied in detail. The subjects on continuous-time linear
systems and general nonlinear systems will also be discussed briefly. Part II
(Chapters 3,4,5) of the textbook covers most of these topics.

Topics:

1. Basic concepts and analysis of linear stochastic systems
1.1. Analysis of discrete-time linear stochastic systems
1.2. Belief discussion on continuous-time linear stochastic systems

2. Optimal state-estimation (filtering) for linear stochastic systems
2.1. Optimal estimation for discrete-time linear systems
2.2. Optimal estimation for continuous-time linear systems
2.3. (Sub)optimal estimation for nonlinear systems

3. System parameters identification
3.1. Discrete-time systems identification
3.2. Hybrid approach for continuous-time systems identification

4. Review of optimal systems control theory and techniques
4.1. Optimal systems control of discrete-time systems
4.2. Optimal systems control of continuous-time systems
4.3. LQ optimal control and Riccati equations

5. Optimal control of linear stochastic systems
5.1. LQG optimal control problems
5.2. LQG optimal control problems with time-delay

6. Adaptive filtering and adaptive control
6.1. Adaptive filtering for discrete-time linear systems
6.2. Adaptive control for discrete-time linear systems

Computer Project: One per semester