SENSIBILITY ANALYSIS USING POLYNOMIAL CHAOS: APPLICATIONS

Abstract

In this paper, we present robustness analysis of Control Systems by means of the Polynomial Chaos Method (PCM). The PCM was firstly conceived by Norbert Wiener to solve some kind of Gaussian stochastic system. The method was improved and generalized to be applied to different kinds of random measures (the Winer-Askey scheme). It consists of expanding candidate solutions in Galerkin polynomials of random variables, which transforms the system in a bigger set off deterministic equations that can be solved by traditional numerical methods. We also present two examples of applications: 1) robustness analysis of a multivariable linear time invariant system under a robust controller and 2) the robustness analysis of a nonlinear system with a feedback linearization controller.