### 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

KTH

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.
*