##
EECI GSC course on LMIs for optimization and control

(Didier Henrion, LAAS-CNRS, Toulouse, France and FEL-CVUT, Prague,
Czech Republic)

### Online course organized by the Department of Information Engineering, Computer Science and Mathematics of the University of L'Aquila, Italy from 26 to 30 April 2021

## Venue and dates

The course is given online. It consists of 14 lectures of 90 minutes each, given
on Monday 26 (2pm-5:30pm), Tuesday 27 (9:30am-1pm and 2pm-5:30pm), Wednesday 28 (2pm-5:30pm), Thursday 29 (9:30am-1pm and 2pm-5:30pm) and Friday 30 April (9:30am-1pm) 2021, following this schedule.
## Documents

The course outline and keywords are described in this document.
Video recordings of the lectures are available below:

Lecture 1 - Introduction to the course and the participants
Lecture 2 (sound only) - Background on convexity and cones
Lecture 3 (sound only) - Geometry of the semidefinite cone
Lecture 4 - Finite-dimensional conic duality
Lecture 5 - Semidefinite programming duality
Lecture 6 - Matlab demo with SeDuMi, MOSEK and YALMIP - scripts
Lecture 7 - Background on measure theory, infinite-dimensional conic duality
Lecture 8 - Positive polynomials and moments, the moment-SOS hierarchy
Lecture 9 - Solutions to exercises and the moment-SOS hierarchy
Lecture 10 - Polynomial optimization - slides with exercises and notes
Lecture 11 - Polynomial optimization continued - Matlab demo with GloptiPoly - scripts
Lecture 12 - Positively invariant sets
- slides with exercises and notes
Lecture 13 - Polynomial optimal control - slides with exercises and notes
Lecture 14 - Polynomial optimal control continued - Matlab demo with GloptiPoly - scripts
The course 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.

## Homeworks and exam

Homeworks are given during the course.
A written examination is available on request.
Certificates of attendance can be provided on request.

Last updated on 30 April 2021.