Basic Information

  • Course Code: EE 622
  • Course Name: Optimal Control Systems
  • Course Offered In: 2023-2024
  • Semester Season: Spring
  • Instructors: Prof Dwaipayan Mukherjee
  • Prerequisites: Requires knowledge of Control Systems, specifically state space modelling, familiarity with Linear Algebra and Calculus
  • Difficulty (1 being easy and 5 being tough): 4

Course Content

Optimal Control Problem: Conditions for minimality, Finite dimension optimization(constrained and unconstrained), Infinte dimension optiminzation Calculus of Variations: Weak and strong extrema, necesaary conditions for weak extrema(Euler Lagrange equations), 2nd order conditons for weak extrema, necesaary conditions for strong extrema (Weierstrass-Erdmann corner conditions, Weierstrass excess function) Formulation of the Maximum Principle: Variational approach, statement of the Maximum Principle, Proof of Maximum Principle and Time optimal control problem HJB equations and LQR: HJB equations and the Value function, sufficient conditions for optimality. Finite and infinte horizon LQR and Riccati equations Bonus: Missile guidance was covered in brief

Feedback on Lectures

The lectures were intresting and usually intense as professor covered a lot of content in a single class. Lectures are mathematically heavy. Attendance is not mandatory but not a good idea to bunk lectures as current lectures are dependent on previous lectures. The professot is very friendly and very approchable for any kinds of doubt related to course content.

Feedback on Evaluations

Course Evaluation: Assignments(4):15% Quizzes(2):20% Midsem:25% Endsem:40% Assignments had lot of questions and a part of them were graded. Solving assignments (the ungraded part also) will definitely help for the exams. Papers are lengthy, calculative and moderately difficult. Scoring in papers is usually tough. 60-70% score was usually considered very good.

Study Material and Resources

The main textbook is Calculus of Variations and Optimal Control Theory:Daniel Liberzon, majority of the content can be found in the book Other books are Optimal Control Theory:Donald Kirk, lectures notes of similar courses can be found online

Follow-up Courses

This is a PG level course so a follow up would be to pursue RnD or SRE under a professor working in similar field. Although courses with similar topics are: EE613:Non Linear Dynamical Systems, EE640:Multivariable Control Systems

Final Takeaway

The course is mathematically intriguing and intellectually challenging. If you are a person who likes solving and thinking about tough problems, this would be a very good course for you. The grading was not that good, and although the course is 6 credits, it demands more work. If your semester is already loaded, then it might get tough to keep up