On experiment design for local approach identification of LPV systems

Abstract

The local approach for the estimation of a Linear Parameter-Varying (LPV) model consists in an interpolation of a finite number of Linear Time-Invariant (LTI) systems called local LTI systems. Each local LTI system is obtained by performing an identification experiment at a fixed constant value of the parameter describing the dynamic variation of the LPV model. This parameter is referred in the literature as scheduling variable and the fixed values of the scheduling variable are simply called operating points or scheduling points. In order to improve the accuracy of the local method for the identification of LPV systems, the choice of the scheduling points and the inputs used at each scheduling point for the identification of the local LTI systems is addressed in this paper. To deal with this problem, an accuracy measure is first introduced. This measure is shown to be a linear combination of the classic A-optimality accuracy measure of the local LTI systems. Using this result, an algorithm is finally proposed to solve the experiment design problem.