Optimization and Systems Theory Seminar
Friday, September 13, 2002, 14.00-15.00, Room 3721, Lindstedtsv. 25

Ryozo Nagamune
Division of Optimization and Systems Theory
Department of Mathematics
E-mail: ryozo@math.kth.se

Robust control with complexity constraint: A Nevanlinna-Pick interpolation approach

The purpose of this talk is to give a survey of my thesis that will be defended on September 20. The thesis consists of five papers that present new techniques and algorithms to design robust controllers of low complexity based on a recent theory of Nevanlinna-Pick interpolation with degree constraint.

First, the necessity of both robust control and complexity constraint is briefly explained. Next, the Nevanlinna-Pick interpolation theory with degree constraint is reviewed, by starting from the classical Nevanlinna-Pick interpolation. To determine each interpolant with a degree bound, we encounter a convex optimization problem. We apply a homotopy continuation method to solve the optimization problem in a numerically robust manner. The continuation method consists of predictor and corrector steps.

We consider two fundamental and important robust control problems. One is the closed-loop shaping problem and the other is the robust regulation problem with robust stability, both of which are reducible to the Nevanlinna-Pick interpolation problem. We apply the Nevanlinna-Pick interpolation theory with degree constraint to these problems, and present a degree bound of controllers for each problem. Some numerical examples are also given.

Calendar of seminars
Last update: September 5, 2002 by Anders Forsgren, anders.forsgren@math.kth.se.