Cleveland State University

Department of Electrical and Computer Engineering

EEC 644 / 744

Optimal Control

There are many ways to design a control system. Adaptive control is a way of allowing a control system to adjust to changes in the system that is being controlled. Fuzzy and neural control allow a designer to control a system without having a mathematical model of the system. Robust Control is a frequency-domain method of designing a control system that is not sensitive to variations in the plant model or noise.

Optimal control is a time-domain method that has been around since the 1950s and has seen a lot of successful applications. Given a system and reference signal that we want the system output to track, what controller will minimize the error between the system output and the reference signal? The dual problem is the problem of estimation: given a system, what state estimator will minimize the error between the true state and the estimated state? The answer to the optimal estimation problem is given by the Kalman filter. Both of these problems will be attacked in this course.

Here are the links to the course syllabus and the homework assignments.

• Syllabus
• Homework Assignments

Here are some sample Matlab programs.

• Ex200.m - This shows the effects of linearization. This is the example that starts at the bottom of page 71 in Stengel’s book.
• ExLQR1.m - This compares the time varying and the time invariant linear quadratic regulator for a 2nd order system.
• Ex36a.m - This shows how to compute an optimal control using gradient descent with analytical derivative computations.
• Ex36b.m - This shows how to compute an optimal control using gradient descent with numerical derivative computations.
• Ex36c.m - This shows how to compute an optimal control using generalized gradient descent.
• Ex43.m - This demonstrates a discrete-time Kalman filter for the altitude measurement of a 3rd order system.

Here are some good links to optimal control web sites.

• Alessandro Astolfi’s Optimal Control Site
• Robert Stengel’s Optimal Control Site
• Sean Meyn's Optimal Control Site
• Anders Rantzer’s Optimal Control Site
• Optimal Control at the University of Illinois

I’ve written an Introduction to Kalman Filtering web site that you can read and get some additional web links from. You can also read a version of a similar article called Kalman Filtering (pdf, 425 KB - postscript, 1.26 MB) that appeared in the magazine Embedded Systems Programming.

This course uses MATLAB a lot and Maple less frequently. You can find more information about MATLAB and Maple from the links below.

• MATLAB Links
• Maple Links

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Professor Simon's Home Page

Department of Electrical and Computer Engineering

Cleveland State University

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Last Revised: November 4, 2002