[Opt-net] Course Announcement

[Didier Henrion]

Course on LMI in Prague - Winter 2009

Course on LMI optimization with applications in control
by Didier Henrion, LAAS-CNRS, Toulouse, France
and Czech Technical University in Prague, Czech Republic.
http://www.laas.fr/~henrion

Venue and dates:
The course is given at the Czech Technical University in Prague,
Charles Square, down-town Prague (Karlovo Namesti 13, 12135 Praha 2)
from Monday February 2 to Friday February 6, 2009. It consists of
six two-hour lectures and two two-hour Matlab labs. There is no
admission fee, students and reseachers from external institutions
are particularly welcome, but please send an e-mail to
<henrion at laas.fr> to register.

Description:
This is a course for graduate students or researchers with some
background in linear algebra, convex optimization and linear control
systems. The focus in on semidefinite programming (SDP), or
optimization over linear matrix inequalities (LMIs), an extension of
linear programming to the cone of positive semidefinite matrices.

Outline:
In the first part of the course, historical developments of LMIs and
SDP are surveyed. Convex sets that can be represented with LMIs are
classified and studied. LMI relaxations are introduced to solve
non-convex polynomial optimization problems, with a focus on the
theory of measures and moments. Finally, interior-point algorithms
are described to solve LMI problems and latest achievements in software
and solvers are reported. The second part of the course focuses on
the application of LMI techniques to solve control problems. Standard
control problems are revisited thanks to recent results on invariant
measures and SDP. Finally, more difficult control problems, such as
robustness analysis of linear systems, or design of fixed-order robust
controllers with H-infinity specifications, are addressed thanks
to the flexibility of the LMI framework. The originality of the approach
is in the simultaneous use of algebraic or polynomial techniques
(as opposed to classical state-space methods) and modern convex
optimization techniques. For the labs we use YALMIP, GloptiPoly,
SeDuMi and PENNON under a Matlab environment.

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Didier HENRION  LAAS-CNRS  7 Av Col Roche  31077 TOULOUSE  FR
Tel:+33561336308 Fax:+33561336936 http://www.laas.fr/~henrion
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