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.