EML 6934 - Optimal Control

Spring 2012

Course Instructor: Dr. Anil V. Rao, MAE-A 314, E-mail: anilvrao@ufl.edu. Tel: 352-392-5523 (Office)

Required Textbook: Kirk, D. E., *Optimal Control Theory: An Introduction,* Dover Publications, 2005.

Syllabus:

- Calculus of Variations
- Calculus of Variations Applied to Optimal Control
- Nonlinear Optimization
- Numerical Methods for Solving Optimal Control Problems

Assignments:

Course Project: The project for the course is as follows. Choose an optimal control problem in your application area of interest. Examples of such areas include chemical engineering, mechanical engineering, aerospace engineering, economics, and medicine. The problem you choose must be nonlinear and must contain a minimum of a four-dimensional state and a two-dimensional control. Furthermore, your problem cannot have an analytic solution. You must provide a complete mathematical description of your optimal control problem. You must then formulate the complete set of first-order optimality conditions for your problem using the calculus of variations. Then, you must solve your problem using at least two different numerical methods that we have studied in the course. Of these methods, one must be an indirect method and the other must be a direct method. In your analysis, consider the following questions. Can you determine the proximity of your numerical solution to the “true” optimal solution. If you are unable to ascertain how close your solution is to the true optimal, how do you know you have obtained a reasonable approximation? What is the computational efficiency of the methods you applied to solve your problem? What are the limitations of the methods you have chosen on your problem. Given your analysis, what numerical method would you seek in order to overcome the deficiencies you found with the methods you chose? It is highly recommended that you now wait until the last minute to think of a problem for your project! The course project is due on 25 April 2012.

Syllabus:

- Exam #1: 30 percent
- Exam #2: 30 percent
- Project: 40 percent