EE622 Optimal Control Systems (Spring 2016)

ANNOUNCEMENTS: HW5 UPLOADED.

 

Instructor: Dr. Debraj Chakraborty

Email: dc [AT] ee.iitb.ac.in

Office: New Office Complex, 1st floor, EE

Lecture Hours: Slot 3 (EEG 002)

Website: http://www.ee.iitb.ac.in/~dc/EE622/

 

TA: 1. Apurva Joshi (apurvajoshi [AT] iitb.ac.in) 2. Sandeep K. T. (sandeep.thilakan [AT] yahoo.com) 3. Mousumi Mukherjee (mousumi_ee [AT] iitb.ac.in

 

Syllabus

1.     Non-Linear Optimization: Unconstrained, Constrained, Lagrange Multipliers, Quadratic Programming, Merit Functions, Line Search, Trust Region Methods, SQP

2.     Dynamic Programming: Principle of Optimality, Computation of Optimal Control using Dynamic Programming, Discrete LQR, Hamilton-Jacobi-Bellman Equation, Continuous LQR

3.     Calculus of Variations: Constraints and End Point conditions

4.     Calculus of Variations approach to Optimal Control Problems: Necessary Conditions, LQR, Indirect methods: TPBVP using Shooting Methods and Collocation

5.     Constrained Optimal Control: Pontryagins Minimum Principle, Min Time, Min Energy, Min Fuel Problems, Singular Arcs

6.     Direct Methods of Computation:

1.     Large Sparse Nonlinear Programs: Sparse Finite Differences, Sparse QP, Sparse SQP, Nonlinear Least Squares

2.     Discretization Methods, Direct vs. Indirect Methods, NLP Considerations

Text Book

No Text Book is prescribed. Lecture Notes will be provided.

Reference Books

  1. Donald E. Kirk, Optimal Control Theory, Prentice-Hall, New Jersey, 1970.
  2. Arthur E. Bryson and Yu-Chi Ho, Applied Optimal Control: Optimization, Estimation and Control, Blaisdell Publishing Company, 1969.
  3. John T Betts, Practical Methods for Optimal Control and Estimation using Nonlinear Programming (2nd ed.), SIAM, 2010.

Evaluation:

Homework assignments will be distributed regularly. The homework assignments will consist of two parts. One part will be based on the theory discussed in class and this part will carry no points. However, the questions in this part will be corrected by the TA. Students are requested to regularly clarify any questions about the homework correction (only) with the TAs. The second part will consist of short programming assignments on the theory discussed in class. This part will be graded and will cumulatively carry 10% weight of the total marks.

There will be one midterm (30%) and one end of semester (50%) final examination. Examination questions will be based on homework problems.

In addition, there will be a computation based term project worth 10% of the total marks. Details about the project are listed below.

Lecture Notes

1.     Lecture 1 : Nonlinear Optimization

2.     Lecture 2: Dynamic Programming

3.     Lecture 3: Calculus of Variations

4.     Lecture 4: Optimal Control

5.     Lecture 5: Numerical Methods

6.     Lecture 6: Optimal Control with Path Constraints

7.     Lecture 6a: PMP Examples (Deepak Patil)

8.     Lecture 7: LQR

9.     Lecture 8: The Kalman Filter

Homework Assignments

1.       Homework 1: Submit by 1st Feb, 2016 in class.

2.       Homework 2: Submit by 16 Feb, 2015 in class

·        Part 1: (Voluntary: No Computer required): From Donald Kirk: (Ref Book 1 above): 3.4,3.6,3.7,3.8,3.10.

·       Part 2: (Compulsory: Computer required): From Donald Kirk: 3.14, 3.23, Example 3.10-1 from Page 84.

3.     Homework 3 (submit by 15/3/16): From Donald Kirk: (Ref Book 1 above): 4.5,4.8,4.10,4.11,4.12,4.15,4.22,4.23,4.24,4.25

4.     Homework 4: From Bryson and Ho (Ref Book 2 above): Sec 2.4: Prob 2, Sec 2.7: Prob 1, 2, 3, 5, 6, 8, 10, 14

5.     Homework 5: From Bryson and Ho (Ref Book 2 above): Sec 3.1: Prob 1, Sec 3.2: Prob 3, Sec 3.9: Prob 3, 4, 5, 6. From Kwakernaak and Sivan, 4.1, 4.2, 4.3. If you submit by  17/4, Sunday (You can slide the solution underneath my office door or directly give it to the TAs in CC lab), then we will correct and return by Monday (collect it from CC lab).

 

 

 

Project:

Please put up your project topics here: http://goo.gl/forms/1jX67FNxd6