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