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