Patrick Schrangl, Laura Giarré,
"On optimal design of experiments for static polynomial approximation of nonlinear systems"
: 2020 American Control Conference (ACC), in Systems & Control Letters, 8-2020

Original Titel:

On optimal design of experiments for static polynomial approximation of nonlinear systems

Sprache des Titels:

Englisch

Original Buchtitel:

2020 American Control Conference (ACC)

Original Kurzfassung:

Models are of great importance for many purposes, including control design. However, most real
systems are complex, frequently nonlinear and first principle models tend to be too complicated, or
even unknown, for control-oriented modeling. Therefore, data-based models are often used; however,
since most likely the true system is not an element of any assumed model class, the available model
is an approximation of the real system. To identify nonlinear systems, universal approximations are
often used, e.g., polynomial nonlinear models whose number of parameters rapidly increases with
model complexity. Because of the high number of parameters to be identified and the presence of
nonlinearity, the accurate choice of an appropriate excitation becomes essential and not trivial. The
aim of the present paper is to analyze classical design of experiment (DOE) and present its limits in
terms of prediction error, for the static polynomial setup under investigation. First, when the system
belongs to the assumed model class, we suggest the use of a more suitable optimization criterion that
we prove to be a generalization of the well-known V-optimality. Second, we show that if we design
the excitation input based on a higher degree model than the one to be identified, it gives rise to a
more efficient approximation.

Sprache der Kurzfassung:

Englisch

Englische Kurzfassung:

Models are of great importance for many purposes, including control design. However, most real
systems are complex, frequently nonlinear and first principle models tend to be too complicated, or
even unknown, for control-oriented modeling. Therefore, data-based models are often used; however,
since most likely the true system is not an element of any assumed model class, the available model
is an approximation of the real system. To identify nonlinear systems, universal approximations are
often used, e.g., polynomial nonlinear models whose number of parameters rapidly increases with
model complexity. Because of the high number of parameters to be identified and the presence of
nonlinearity, the accurate choice of an appropriate excitation becomes essential and not trivial. The
aim of the present paper is to analyze classical design of experiment (DOE) and present its limits in
terms of prediction error, for the static polynomial setup under investigation. First, when the system
belongs to the assumed model class, we suggest the use of a more suitable optimization criterion that
we prove to be a generalization of the well-known V-optimality. Second, we show that if we design
the excitation input based on a higher degree model than the one to be identified, it gives rise to a
more efficient approximation.