5B1872 Optimal Control, 4 p, spring 2006

Examiner and lecturer

Ulf Jönsson (ulfj@math.kth.se), room 3711, Lindstedtsv. 25, phone. 790 84 50.

Teaching assistant

Johan Karlsson (johan.karlsson@math.kth.se), room 3726, Lindstedtsv. 25, phone. 790 75 07.

Course material

Lecture notes: Will be sold at "institutionens elevexpedition", Lindstedtsv. 25. The price is 50 Kr.
Exercise material: Will be sold at "institutionens elevexpedition", Lindstedtsv. 25. The price is 40 Kr.

Course content
The goal of the course is to present the main results of continuous time optimal control.

Dynamic Programming Discrete dynamic programming, principle of optimality, Hamilton-Jacobi-Bellman equation, verification theorem.

Pontryagin minimum principle Several versions of Pontryagin Minimum Principle (PMP) will be discussed.

Infinite Horizon Optimal Control Optimal control over an infinite time horizon, stability, LQ optimal control.
Applications Examples from economics, logistics, aeronautics, and robotics will be discussed.

Computational Algorithms The most common methods for numerical solution of optimal control problems are presented.

Examination
Written exam where you may use Beta Mathematics Handbook and the following formula sheet (ps) (pdf) ). The exam will take place on Thursday, March 9 at 8.00 - 13.00 in the rooms E33,E34.
Solutions to exam on March 9, 2006 (pdf)

There will be two optional homework sets during the course. They give maximally 3 bonus credits on the exam. The exam will consist of five problems that give a maximum of 25 credits (not including your bonus credits from the homework sets). The grading rule for the exam is that 12 credits guarantee grade 3, 17 credits guarantee grade 4, and 22 credits guarantee grade 5.

Homework set 1 will be due at 17.00 February 7, 2006. Here is the file [pdf].
Homework set 2 will be due at 17.00 February 27, 2006. Here is the file [pdf].
The homework sets will also be posted on this web page.
Matlab code
Here are some Matlab routines that are used in the excerise notes. You may use this for the solution of your homeworks.

Dynamic programming (Tracking with B747). Matlab files [fRic.m,fSys.m,PtoX.m,XtoP.m,mainRic.m]

Computational Algorithms (Shooting method for the orbit transfer problem). Matlab files [appr_dfdx.m,fh.m,main.m,newton_solver.m,plotresults.m,theta.m]

Preliminary schedule
Optimal control problems

L/E Day Date Time Room Topic

L1. Wed 18/1 10-12 E31 Introduction

L2. Thu 19/1 15-17 D33 Discrete dynamic programming

L3. Mon 23/1 13-15 D35 Discrete dynamic programming [pdf]

E1 . Tue 24/1 15-17 E34 Dynamic programming (I)

L4. Wed 25/1 10-12 D33 Optimal Control Problems

L5. Thu 26/1 15-17 E33 Dynamic programming

L6. Mon 30/1 13-15 D35 Dynamic programming

E2. Tue 31/1 15-17 E34 Dynamic programming (II)

L7. Wed 1/2 10-12 E31 Mathematical Preliminaries (Linear systems)

L8. Thu 2/2 15-17 E33 Mathematical preliminaries (ODE theory etc)

L9. Mon 6/2 13-15 D35 Pontryagins minimum principle (PMP) (using small variations)

L10. Tue 7/2 15-17 E34 PMP (control constraints)

L11. Thu 9/2 15-17 E33 PMP (optimal control to a manifold)

E3. Mon 13/2 13-15 D35 PMP I.

E4. Tue 14/2 15-17 E34 PMP II: Time optimal control

L12. Thu 16/2 15-17 D33 PMP (generalizations)

L13. Mon 20/2 13-15 D35 PMP (applications)

E5. Tue 21/2 15-17 E34 PMP III.

E6. Thu 23/2 15-17 E33 PMP IV

L14. Mon 27/2 13-15 D35 Infinite time horizon optimal control

E7. Tue 28/2 15-17 E34 Infinite time horizon optimal control

L15. Thu 2/3 15-17 E33 Computational algorithms

Welcome!
Further information is available at http://www.math.kth.se/optsyst/studinfo/5B1872/.
5B1872 Optimal control
Last modified: October, 2005 by Ulf Jönsson, ulfj@math.kth.se.

L/E	Day	Date	Time	Room	Topic
L1.	Wed	18/1	10-12	E31	Introduction
L2.	Thu	19/1	15-17	D33	Discrete dynamic programming
L3.	Mon	23/1	13-15	D35	Discrete dynamic programming [pdf]
E1 .	Tue	24/1	15-17	E34	Dynamic programming (I)
L4.	Wed	25/1	10-12	D33	Optimal Control Problems
L5.	Thu	26/1	15-17	E33	Dynamic programming
L6.	Mon	30/1	13-15	D35	Dynamic programming
E2.	Tue	31/1	15-17	E34	Dynamic programming (II)
L7.	Wed	1/2	10-12	E31	Mathematical Preliminaries (Linear systems)
L8.	Thu	2/2	15-17	E33	Mathematical preliminaries (ODE theory etc)
L9.	Mon	6/2	13-15	D35	Pontryagins minimum principle (PMP) (using small variations)
L10.	Tue	7/2	15-17	E34	PMP (control constraints)
L11.	Thu	9/2	15-17	E33	PMP (optimal control to a manifold)
E3.	Mon	13/2	13-15	D35	PMP I.
E4.	Tue	14/2	15-17	E34	PMP II: Time optimal control
L12.	Thu	16/2	15-17	D33	PMP (generalizations)
L13.	Mon	20/2	13-15	D35	PMP (applications)
E5.	Tue	21/2	15-17	E34	PMP III.
E6.	Thu	23/2	15-17	E33	PMP IV
L14.	Mon	27/2	13-15	D35	Infinite time horizon optimal control
E7.	Tue	28/2	15-17	E34	Infinite time horizon optimal control
L15.	Thu	2/3	15-17	E33	Computational algorithms