Division of Optimization and Systems Theory
Department of Mathematics
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.