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. Classical control methods are based on undergraduate material in the time domain (PID control) or in the frequency domain (Bode plots, Nyquist plots, and so on). Adaptive control is designed to adjust to changes in the system being controlled. Fuzzy and neural control systems are designed without a mathematical model of the system. Robust control is designed to be insensitive to noise or to variations in the system.

Optimal control is a time-domain method based on state-space models and was developed in the late 1950s for aerospace systems during the space race between the US and the USSR. It has seen a huge number of successful applications, and continues to provide practical solutions to wide variety of systems. An optimal controller minimizes 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 links to good optimal control web sites.

- Optimal Control at Princeton, by Robert Stengel
- Optimal Control at the University of Illinois, by F. B. Hansen
- 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, by Victor Becerra, 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 Engineering and Computer Science

Last Revised: January 9, 2018