On joint optimal experiment design for identifying partition and local model parameters of Takagi-Sugeno models

Abstract

Optimal Experiment Design (OED) is a well-developed concept for regression problems that are linear-in-their-parameters or for linear dynamical models. In case of nonlinear Takagi-Sugeno models either non-model-based experiment design or OED restricted to the local model parameters has been examined. This article proposes to a joint design of local model and partition parameters that bases on the Fisher Information Matrix (FIM). For this purpose, a symbolic description of the joint FIM is derived. Its heterogeneous structure can make it badly conditioned, complicating computation of its determinant for a D-optimal design. This problem is relaxed using determinant decomposition. A theoretical analysis and a case study show that optimal experiment designs for local model and for partition related parameters may significantly differ from each other.