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 2006

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 13 to Friday February 17, 2006 and from Monday February 20 to Friday February 24, 2006.

Each course consists of five two-hour lectures (10am to 12am in room K24 of building E, except on Tuesday February 21 in room G205 of building G) and three two-hour labs (2pm to 4pm in room K2 of building E). When entering the main building from the metro and tramway station of Charles Square (Karlovo Namesti) follow the black arrows to building E (Faculty of Electrical Engineering). Building E is labelled F3 on this campus map.

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.

Contact Didier Henrion if you are interested in attending the courses.

Outline

The expected audience are 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 (D. Henrion, Feb 13-17, 2006)

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 - LMIs in control
    II.1 - State-space methods - stability analysis: Lyapunov stability, pole placement in LMI regions, uncertain systems and robustness analysis
    II.2 - State-space methods - control design: H2, Hinf, robust state-feedback and output-feedback design
    II.3 - Polynomial methods - stability analysis: polynomials in control, robust stability of polynomials
    II.4 - Polynomial methods - control design: robust fixed-order controller design

    Second course (M. Kocvara, Feb 20-24, 2006)

  • Part III - Algorithms
    III.1 - Algorithms for convex optimization: general introduction, interior-point methods, primal-dual methods
    III.2 - Algorithms for linear SDP: implementation, solvers, interfaces
    III.3 - Generalized augmented Lagrangian method for convex SDP: PENNON software, algorithm, implementation details

  • Part IV - BMIs in control and mechanics
    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.

    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

    Many thanks to (in alphabetical order) Wouter Aangenent, Petr Augusta, Bjoern Bukkems, Blazej Cichy, Lukasz Hladowski, Ondrej Holub, Otakar Sprdlik, Bartek Sulikowski, Jiri Trdlicka, Marten Voelker, Gert Witvoet and Fuweng Yang for their feedback and comments that will be taken into account when preparing next versions of this course.

    Last updated on 13 December 2006