ECE553: Optimum Control Systems

Course Information

  • Office Hours: Th 1-2pm, 145 CSL

  • Lectures: T/Th 2:00-3:20pm, Room 4070 ECEB

  • TA's Office Hours: Wed 4-5pm, 164 CSL

  • For a complete syllabus, see here.

  • Announcements will be done through Piazza.

Course Description

This is a graduate-level course on optimal control systems. It presents a rigorous introduction to the theory of calculus of variations, the maximum principle, and the HJB equation. The course deals mainly with general nonlinear systems, but the linear theory will be examined in detail towards the end.


  • Introduction (1.5 week)

  • Calculus of variations (3 weeks)

  • The maximum principle (5 weeks)

  • Hamilton-Jacobi-Bellman equation (2 weeks)

  • LQR problems (1 week)

  • Other topics (time permitting)

Required Materials

We will follow “Calculus of Variations and Optimal Control Theory: A Concise Introduction” by D. Liberzon. A few minor errors are listed “here.


ECE 515; ECE 528 or Math 447 is recommended, but not required.


10% class participation; 60% homework (8 sets); 30% final exam

Homework: There are roughly 8 homework assignments. Each assignment will include five exercise problems from Prof. Liberzon's book. Use entry code 7G776W to add the course on Gradescope where you will be submitting assignments. Discussion on homework problems is permitted, however each student must write and submit independent solutions. Extensions will be granted with instructor approval in advance. Otherwise late homeworks without such prior approval will not be accepted. The two lowest ones of your homework grade will be dropped when calculating the final grade.

Gradescope submission: Read about how to submit assignments on Gradescope here. Make sure your written work is legible. If the TA cannot read your work, then there is no way to grade it. Then the TA may ask you to resubmit or dock points off. Do upload high quality PDF scans; most modern smartphones have a document scanning functionality. Make sure to use the tools in Gradescope to mark where in your upload the answer to each question can be found. Start each question on a new page. For a multi-page answer, associate all relevant pages with the question. You are encouraged to typeset the homework. But this is not required.