Syllabus

Module-1: Static Optimization: unconstrained and constrained cases, Lagrange multiplier, Solution
methods: simplex, interior point. (10 hours)
Module-2: Dynamic programming, Hamilton-Jacobi-Bellman equation Lagrange, Mayer and Bolza
formulations for optimal control problems. (8 hours)
Module-3: Calculus of variations, Linear regulator and tracking problem, matrix Riccati equation and its
solution. (10 hours)
Module-4: Pontryagin’s principle and control problems with constraints on states and control.
minimum time, minimum energy and minimum control-effort problems. (6 hours)
Module-5: Extend the optimal control methods for stochastic systems. (3 hours)

The course will provide an understanding of constrained and unconstrained optimization problems.

The course will provide an understanding of control problems using central mathematical techniques such as calculus of variation and dynamic programming.

The course will provide an understanding of the main results in optimal control and how they are used in various applications.

At the end of the course, students will be able to
CO1: Demonstrate basic knowledge in the field of static and dynamic optimization.
CO2. Demonstrate basic knowledge in the field of dynamic programming and variational calculus to find an optimal path.
CO3. Formulate and solve optimal control problems based on dynamic constraint and objective function specifications.
CO4. Solve optimal control problems with static constraints.
CO5. Analyze optimal control for stochastic systems.
CO6. Use computational tools to implement the methods specified in the course.

Donald E Kirk, Optimal Control Theory: An Introduction, Dover , 2016

M. Athans and P.L. Falb, Optimal Control, McGraw Hill , 2007

A. E. Bryson, Yu-Chi Ho, Applied optimal Control: Optimization, Estimation and Control, Taylor & Francis , 2016

R. F. Stengel, Optimal Control and Estimation, Dover , 1994