Optimization and Systems Theory Seminar
Friday, April 4, 2003, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Chung-Yao Kao
Institut Mittag-Leffler
Djursholm, Sweden
E-mail: cykao@alum.mit.edu

Efficient computational algorithms for IQC analysis

Issues of robust stability and performance have dominated the field of systems and control theory because of their practical importance. The recently developed, Integral Quadratic Constraint (IQC) based analysis method provides a framework for systematically checking robustness properties of large complex dynamical systems. In IQC analysis, the system to be analyzed is represented as a nominal, Linear Time-Invariant (LTI) subsystem interconnected with a perturbation term. The perturbation is characterized in terms of IQCs. Checking the condition for robustness is formulated as solving a particular infinite dimensional optimization problem.

The conventional way of solving this type of optimization problems is to transform them into Semi-Definite Programs (SDPs) which are then solved using interior-point algorithms. The disadvantage of this approach is that the transformation introduces additional decision variables. In many situations, these auxiliary decision variables become the main computational burden, and the conventional method then becomes very inefficient and time consuming. In this talk, a number of specialized algorithms for solving optimization problems arising from IQC analysis are presented. The crucial advantage of these newly developed algorithms is that no auxiliary decision variables are introduced. The results of our numerical experiments confirm that these algorithms can solve a problem arising from IQC analysis much faster than the conventional approach does.

Calendar of seminars
Last update: March 10, 2003 by Anders Forsgren, anders.forsgren@math.kth.se.