D-Optimal Design for Information Driven Identification of Static Nonlinear Elements

Abstract

Identification of static nonlinear elements (i.e., nonlinear elements whose outputs depend only on the present value of inputs) is crucial for the success of system identification tasks. Identification of static nonlinear elements though can pose several challenges. Two of the main challenges are: (1) mathematical models describing the elements being unknown and thus requiring black-box identification; and (2) collection of sufficiently informative measurements. With the aim of addressing the two challenges, we propose in this paper a method of predetermining informative measurement points offline (i.e., prior to conducting experiments or seeing any measured data), and using those measurements for online model calibration. Since we deal with an unknown model structure scenario, a high order polynomial model is assumed. Over fit and under fit avoidance are achieved via checking model convergence via an iterative means. Model dependent information maximization is done via a D-optimal design of experiments strategy. Due to experiments being designed offline and being designed prior to conducting measurements, this method eases off the computation burden at the point of conducting measurements. The need for in-the-loop information maximization while conducting measurements is avoided. We conclude by comparing the proposed D-optimal design method with a method of in-the-loop information maximization and point out the pros and cons. The method is demonstrated for the single-input-single-output (SISO) static nonlinear element case. The method can be extended to MISO systems as well.