Embedded and Convex Optimization for Control

Stephen Boyd and Moritz Diehl

Leuven, 15-19 March 2010

COURSE INFORMATION

The course Embedded and Convex Optimization for Control is an interactive course to provide the participants with a strong working knowledge about the methods and applications of dynamic optimization in engineering applications. The course will consist of lectures, interactive sessions and guided computer exercises and is organized in Leuven as part of the ATHENS program 15 to 19 March 2010. It is aimed at 5th year master students with very strong skills in mathematics and programming in the languages C++ and MATLAB.

There will be applications from several fields that are treated in self-chosen tutorial projects by the participants in the last two days of the course. Particular emphasis is put on convex and embedded optimization.

The goal is that towards the end of the course, every participant will be working on formulating and solving a dynamic optimization problem of her/his own choice, so it is encouraged to think about interesting applications of dynamic optimization even before the course starts. The lectures and exercises will be given by S. Boyd, M. Diehl, B. Houska, H.J. Ferreau, J. Mattingley, and Y. Wang.

The language of the course is English.

Prerequisites

Strong background in analysis and linear algebra corresponding to the first two years of a science or engineering degree with good grades. Knowledge of numerical mathematics is very helpful, but not manditory.
Programming skills in the languages Matlab and C++ are needed.

Topics covered in the course

Convex optimization problems and interior point algorithms
Theory of nonlinear programming and optimal control
Dynamic system modeling for optimization
Model Predictive Control
Convex optimization with the open-source package CVX - a matlab software for disciplined convex programming.
Dynamic optimization using the open-source software package ACADO Toolkit - a toolkit for automatic control and dynamic optimization developed by OPTEC

Examination

A short written exam for self-assessment and rehearsal will be held on Friday morning

Location

K.U. Leuven, Celestijnenlaan 200A (google maps), PC Room 00.124 and Seminar Room 00.144. The course will take place Mo-Fr 9:00 - 17:30

Accomodation

See Visitor Information.

The Program at a Glance:

	Monday 15	Tuesday 16	Wednesday 17	Thursday 18	Friday 19
9:00 - 10:30	Introduction to Nonlinear Optimization M.Diehl	Lecture on Dynamic Processes with Computer Exercise M. Diehl, B. Houska, H.J. Ferreau	Demonstration at the Department of Mechanical Engineering	Team-Work on Self Chosen Projects: Convex Optimal Control	WRITTEN EXAM
10:45-12:15	Recent Advances in Convex Optimization S. Boyd	Convex Optimization Methods for Stochastic Control Y. Wang	Computer Exercises: Solving Optimal Control Problems with ACADO B. Houska and H.J. Ferreau	Team-Work on Self Chosen Projects: Convex Optimal Control	Student Presentations of the Self Chosen Projects
	Lunch	Lunch	Lunch	Lunch	Lunch together
13:30-15:00	Convex Sets, Functions,and Problems Y. Wang	Nonlinear Optimal Control M. Diehl	Automatic code generation for real-time convex optimization J. Mattingley	Team-Work on Self Chosen Projects: Nonlinear Optimal Control	Student Presentations of Self Chosen Projects 13:00-14:00
15:15-16:15	Computer Exercise: CVX Tutorial J. Mattingley	Nonlinear Programming M. Diehl	Computer Exercise on Nonlinear Model Predictive Control H.J. Ferreau and B. Houska	Team-Work on Self Chosen Projects: Nonlinear Optimal Control	Reception at Arenberg Castle
16:30-17:30	Office Hours: Time for Questions	Office Hours: Preparation of the Projects for Thursday	Nonlinear Model Predictive Control M. Diehl	free	Reception at Arenberg Castle

DETAILED PROGRAM:

Program on Monday, 15/3/2010

Time	Topic	Room
09.00 - 09.15	Welcome by the organizers Moritz Diehl	00.124
09.15 - 9.45	Introduction to Embedded Optimization for Control Moritz Diehl	00.124
9.45 - 10:30	Optimization: An Overview Moritz Diehl	00.124
10.30 - 10.45	Coffee break	close to 00.124
10.45 - 12.15	Recent Advances in Convex Optimization Stephen Boyd	00.124
12.15 - 13.30	Lunch break	ALMA 3
13.30 - 15.00	Convex Sets, Functions, and Problems Yang Wang	00.124
15.00 - 15.15	Coffee break	close to 00.124
15:15 - 15:45	Convex Functions and Sets Yang Wang	00.124
15.45 - 16.45	Disciplined Convex Programming and CVX Interactive Lecture and Demonstration Jacob Mattingley and Yang Wang	00.124
16:45 - 17:00	short break
17.00 - 17:30	office hours, time for questions	00.124

Program on Tuesday, 16/3/2010

Time	Topic	Room
09.00 - 09.25	Dynamic Process Models Moritz Diehl	00.124
09.25 - 9.45	Numerical Simulation of ODE models Boris Houska	00.124
9.45 - 10:30	ACADO exercise: Simulation of a Crane Model Boris Houska and Hans Joachim Ferreau	00.124
10.30 - 10.45	Coffee break	close to 00.124
10.45 - 11.45	Convex Optimization Methods for Constrained Linear Stochastic Control Yang Wang	00.124
11.45 - 12.15	Exercise using CVX for MPC Jacob Mattingley	00.124
12.15 - 13.30	Lunch break	ALMA 3
13.30 - 15.00	Numerical Optimal Control Moritz Diehl	00.144
15.00 - 15.15	Coffee break	close to 00.144
15.15 - 16.15	Newton Type Constrained Optimization in a Nutshell Moritz Diehl	00.144
16:15 - 16:30	short break
16.30 - 17:30	Preparation of the Projects for Thursday. Individual discussion with one of the teachers.	00.144

Program on WedNesday, 17/3/2010

Time	Topic	Room
09.00 - 09.30	Introduction to Mechanical Engineering Applications Moritz Diehl	00.124
09.30 - 10.30	Visit at the Department of Mechanical Engineering Lieboud Van den Broek, Jan Swevers, Moritz Diehl	PMA
10.30 - 10.45	Coffee break	close to 00.124
10.45 - 11.45	Solving Optimal Control Problems with ACADO With Computer Exercise Boris Houska and Joachim Ferreau	00.124
11.45 - 13.00	Lunch break	ALMA 3
13.00 - 14.45	Embedded Convex Optimization Lecture and Computer Exercise Jacob Mattingley	00.124
14.45 - 15:15	Computer Exercise on Nonlinear (Part 1) Model Predictive Control Boris Houska and Hans Joachim Ferreau	00.124
15.15 - 15.30	Coffee break	close to 00.124
15.30 - 16.15	Computer Exercise on Nonlinear (Part 2) Model Predictive Control Boris Houska and Hans Joachim Ferreau	00.124
16:15 - 16:30	short break
16.30 - 18:00	Nonlinear Model Predictive Control Moritz Diehl	00.144

Program on THUrsday, 18/3/2010

Time	Topic	Room
09.00 - 10.30	Team Work on Self Chosen Projects: Convex Optimization for Control Stephen Boyd, Jacob Mattingley, and Yang Wang	00.026
10.30 - 10.45	Coffee break	close to 00.026
10.45 - 12.15	Team Work on Self Chosen Projects: Convex Optimization for Control Stephen Boyd, Jacob Mattingley, and Yang Wang	00.026
12.15 - 13.30	Lunch break	ALMA 3
13.30 - 15.00	Team Work on Self Chosen Projects: Nonlinear Optimal Control Moritz Diehl, Boris Houska, and Joachim Ferreau	00.026
15.00 - 15.15	Coffee break	close to 00.026
15.15 - 16.15	Team Work on Self Chosen Projects: Nonlinear Optimal Control Moritz Diehl, Boris Houska, and Joachim Ferreau	00.026
16:15 - 16:30	short break
16.30 - 17:30	free, learing for exam, or finishing project	00.026

Program on Friday, 19/3/2010

Time	Topic	Room
09.00 - 10.30	WRITTEN EXAM	00.124
10.30 - 10.45	Coffee break	close to 00.124
10.45 - 12.00	Presentation of the Student Projects	00.124
12.00 - 13.00	Lunch break	ALMA 3
13.00 - 14.00	Presentation of the Student Projects	00.124
15.00 - 18.00	Reception	Arenberg Castle

Note that the final programme might be subject to minor changes.

LECTURES / SLIDE MATERIAL:

http://www.stanford.edu/class/ee364a/lectures.html - Lectures by Stephen Boyd
http://www.stanford.edu/class/ee364b/lectures.html - Lectures by Stephen Boyd

MATERIAL FOR THE EXERCISES

CVX - A matlab software for disciplined convex programming

ACADO Toolkit - An open source toolkit for automatic control and dynamic optimization.

CONTACT

Boris Houska
Optimization in Engineering Center (OPTEC), K.U.Leuven,
Electrical Engineering Department (ESAT),
Kasteelpark Arenberg 10 - bus 2446, BE-3001 Leuven-Heverlee,
Belgium

Office : 02.05
Phone: +32 (0)16 32 03 64
E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

LINKS

ATHENS Program
OPTEC Homepage
ATHENS Course 2007
ATHENS Course 2009

TEACHERS

Prof. Stephen P. Boyd
Information Systems Laboratory,
Department of Electrical Engineering,
Stanford University
Phone: (650) 723-0002
E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

Prof. Moritz Diehl
Optimization in Engineering Center (OPTEC) and
Electrical Engineering Departments (ESAT)
K.U. Leuven
Kasteelpark Arenberg 10, 3001 Leuven-Heverlee,
Belgium
E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it
Phone: +32-16-321884

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