Optimal polytopic control system design

Abstract

Polytopic linear models (PLM) are models with parameters that vary within a polytope of the model parameter space, where the vertices of the polytope are defined by the parameters of locally valid linear models. These PLMs are also known as fuzzy models, local model networks or multimodels. In this paper a novel regulator design method for PLM is suggested and formalized. Controller synthesis is based upon optimal control theory. It is shown that under controllability assumptions a solution exists to the Hamilton Jacobi Bellman (HJB) equation, which is known to be a sufficient condition for optimality of the closed loop system. An optimal static state feedback controller can then be computed as a solution of a convex optimization program. It turns out that the optimal control system has an infinite gain margin, a prerequisite for robustness of the control system. The controller design method is illustrated with an example.