Two courses on LMI and BMI optimization with algorithms and
applications in control
(Didier Henrion, LAAS-CNRS, Toulouse, France and Michal Kocvara,
FEL-CVUT, Prague, Czech Republic)
Czech Technical University,
Prague, Czech Republic - February 2005
Venue and dates
The two courses are given at the Czech Technical University, Charles
Square, down-town Prague (Karlovo Namesti 13, 12135
Praha 2) from Monday February 14 to Friday February 18, 2005
and from Monday February 21 to Friday February 25, 2005.
Each course consists of five two-hour lectures (10am to 12am the first
week, 9am to 11am the second week) and three
two-hour labs (2pm to 4pm both weeks).
Registration
The course is primarily aimed at students from the Czech Technical
University in Prague. External participants are welcome, but a
registration fee
(50 euros for one course and 100 euros for both
courses, on-site payment in cash) is required.
Please note
that the Czech Technical University will not provide assistance
regarding travelling and accomodation in Prague.
Contact Didier Henrion
if you are interested in attending the courses.
Outline
The courses at aimed at graduate students or researchers
with a background in linear control
systems, linear algebra and convex optimization.
See a more recent version of the course
for downloadable lecture slides.
First course (Feb 14-18, 2005)
I.0 - General introduction:
course outline and material
Part I - LMI and BMI
I.1 - What is an LMI ?:
history, convexity, cones, duality, semidefinite
programming and applications
I.2 -
Geometry of LMI sets:
convex semialgebraic sets, conic and LMI
representable sets, lift and project techniques
I.3 -
What is a BMI ?:
history, applications
I.4 -
LMI relaxations:
Shor's relaxation, polynomial moments
and sum-of-squares, hierarchy of LMI relaxations
Part II - Algorithms
II.1 -
Algorithms for convex optimization:
general introduction,
interior-point methods, primal-dual methods
II.2 -
Algorithms for linear SDP:
implementation, solvers, interfaces
II.3 -
Generalized augmented Lagrangian method for convex SDP:
PENNON software, algorithm, implementation details
Second course (Feb 21-25, 2005)
Part III - LMIs in control
III.1 -
State-space methods - stability analysis: Lyapunov stability,
pole placement in LMI regions, uncertain systems and robustness analysis
III.2 -
State-space methods - control design: H2, Hinf, robust
state-feedback and output-feedback design
III.3 -
Polynomial methods - stability analysis: polynomials in control,
robust stability of polynomials
III.4 -
Polynomial methods - control design: robust fixed-order
controller design
Part IV - BMIs in control
IV.1 -
Optimization problems with BMIs: problem statement, methods
IV.2 -
Generalized augmented Lagrangian method for nonconvex SDP: PENNON
software, algorithm, implementation details
IV.3 -
BMI problems in control theory: static-output feedback,
simultaneous stabilization, numerical results
IV.4 -
Design of stable mechanical structures: structural design, truss
design, free material optimization, vibration control, stability
control
Homeworks and Labs
Homeworks are handed out during the course.
Some of this material is used during the labs.
See Michal Kocvara's labs for
this course.
For the labs we use the Polynomial Toolbox, PENBMI and the YALMIP
interface to define and solve LMI and BMI problems under the Matlab
environment.
Acknowledgements
Sincere thanks to Hamid Khatibi for his constructive comments.
We are also grateful to (in alphabetical order) Petr Kujan, Andrea
Pome, Bartomiej Sulikowsi, Nikos Triandafyllidis, Pavel Trnka, Maciej
Twardy and Jiri Zikmund for their feedback.
Last updated on 13 December 2006