Cleveland State University

Department of Electrical
Engineering and Computer Science

EEC 644/744, Optimal Control
Systems

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 insensitive to variations in the plant model or noise.

Optimal control is a time-domain method based on state space models, and was first developed in the 1950s. It has seen a lot of successful applications, especially in aerospace. 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, while also minimizing the control effort?

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

Here are some sample MATLAB programs. Check back for updates during the course.

- MotorNominal.m - This is a simulation of nonlinear motor equations.
- Motor.m - This shows the effect of linearization for a motor simulation.
- MotorGeneral.m - This shows how to write general dynamic simulation code.
- Pendulum.m - This shows a linearized simulation of an inverted pendulum.
- tdp1.m - Thrust direction programming
- Gradient.m - Optimal control solution using gradient descent
- GenGradient.m - Optimal control solution using generalized gradient descent
- VariationExtremals.m - Optimal control solution using variation of extremals

Here are some good links to optimal control web sites.

- Robert Stengel's Optimal Control Site
- Optimal Control at the University of Illinois
- An Introduction to Mathematical Optimal Control Theory, by Lawrence C. Evans
- Principles of Optimal Control, by Jonathan P. How
- Optimal Control Theory, by Emanuel Todorov
- A Child's Guide to Optimal Control Theory, by Martin Boileau
- Optimal Control, Scholarpedia
- Calculus of Variations and Optimal Control Theory, by Daniel Liberzon

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

Department of Electrical and Computer Engineering

Last Revised: August 24, 2015