**Academic Year** : Spring 18

**Instructor** : Prof. Madhu Belur

**Motivation** : This course gives an introduction to the traditional methods of optimal control. It is the first course to be done which introduces the concept of optimization within control. It gives way to many advanced courses in optimal control.

**Course content:**

Introduction. static and dynamic optimization. Parameter optimization.;Calculus of Variations : problems of Lagrange,. Mayer and Bolza. Euler-Language equation and transversality conditions, Lagrange multipliers;Pontryagin’s maximum principle; theory; application to minimum time, energy and control effort problems, and terminal control problem.;Dynamic programming : Bellman’s principle of optimality, multistage decision processes. application to optimal control.;Linear regulator problem : matrix Riccati equation and its solution, tracking problem.;

**Structure**:

Quiz 1 : 10 %

Mid Sem : 25 %

Quiz 2 : 25 %

Endsem : 40 %

**Prerequisites** :

There are no hard prerequisites for taking the course. However, the course assumes the basic knowledge of control systems. Hence, it is suggested by the professor that you take the course only after having done a basic Control Systems course.

**Feedback on Lectures** :

The lectures were relatively slow paced, but it was necessary to pay attention. The differences in the methods of solving an optimal control problems mentioned above are very subtle and can be understood only after paying attention and solving example problems. All the methods reduce to each other and understanding the base idea in each is very important.

**Feedback on Exams** :

The exams were mainly based on the assignments that were given and partially solved in class. Having solved the assignments thoroughly, the exams seemed to be on the easy side. Without the assignments it would have been difficult. The checking of papers was a bit lenient and marks were awarded for attempts made.

**Grading**:

Please have a look on ASC for the same.

**Attendance** :

No attendance rule was enforced.

**Textbooks** :

Calculus of Variations and Optimal Control Theory: A Concise Introduction, Daniel Liberzon.

**Future direction** :

This course gives enough introduction to optimization so that one can take up research projects and won’t find trouble regarding the basics while surveying the literature.

Reviewed by :

Karan Chadha (karanchadhaiitb@gmail.com)