Course on LMI optimization with applications in control
(Didier Henrion, LAAS-CNRS, Toulouse, France and FEL-CVUT, Prague,
Czech Republic)
Czech Technical University,
Prague, Czech Republic - 29 November - 1 December 2022
Venue and dates
The course is given at the Charles Square campus of the
Czech Technical University, in the historical center of
Prague (Karlovo Namesti 13, 12135
Praha 2).
It consists of six two-hour lectures, given on Tuesday 29, Wednesday 30 November, and Thursday 1 December 2022,
from 10am to noon and from 2pm to 4pm.
The course is given in room E-24, ground floor on your left hand side
when entering building E.
Please refer to these maps
for instructions to reach this building. The campus entrance
is restricted to badge holders, so please ask the doorperson
to let you in through the electronic gates.
Registration
The course is primarily aimed at students from the Czech Technical
University in Prague, yet external participants are welcome. There is
no registration fee. Please note that the Czech Technical University
will not provide assistance regarding traveling and accomodation in
Prague.
Description
This is a course for graduate students or researchers
with a background in linear control
systems, linear algebra and convex optimization.
Outline and lecture notes
The beginning of the course (mathematical background on convex cones, semidefinite optimization, moments and sums of squares) closely follows the lecture notes:
D. Henrion. Optimization on linear matrix inequalities
for polynomial systems control. International Summer School of Automatic Control, Grenoble, France, September 2014.
Then the course focuses on:
polynomial optimization, see these slides and notes;
maximal positively invariant sets, see these slides and notes;
polynomial optimal control, see these slides and notes.
The material on polynomial optimal control and HJB inequalities can be found in this document:
D. Henrion, E. Pauwels. Linear conic optimization for nonlinear optimal control. Chapter 10 on pages 121-134 in S. Ahmed, M. Anjos, T. Terlaky (Editors). Advances and Trends in Optimization with Engineering Applications. MOS-SIAM series, SIAM, Philadelphia, 2017.
The material on approximating the maximal positively invariant sets of polynomial control systems can be found in this document:
M. Korda, D. Henrion, C. N. Jones. Convex computation of the maximum controlled invariant set for polynomial control systems. SIAM Journal on Control and Optimization, 52(5):2944-2969, 2014.
Illustrative Matlab codes using YALMIP and GloptiPoly can be found here: demo1.zip, demo2.zip, demo3.zip.
Homeworks and exam
Homeworks are given during the course.
A written examination can be organized.
Certificates of attendance can be provided on request.
Last updated on 1 December 2022.