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On robust experiment design for identifying locally affine Takagi-Sugeno models

Optimal experiment design (OED) is a well-developed concept for linear regression and linear dynamical modeling problems. In case of nonlinear models, the dilemma is that in order to evaluate the Fisher Information Matrix (FIM) for experiment design, the parameters to be estimated are required to evaluate the FIM. In case of locally affine Takagi-Sugeno (TS) models and D-optimal designs, even a ‘robust’ sequential OED may not be sufficiently robust against wrong assumptions on partition parameters. As remedy, a two stage experiment design is proposed: It uses a space-filling design to estimate good initial TS model parameters. These are used to initialize a robust sequential FIM-based OED. The method is demonstrated for a nonlinear regression problem.