Reference:
L. Gharavi,
B. De Schutter, and
S. Baldi,
"Parametric piecewise-affine approximation of nonlinear systems: A
cut-based approach," Proceedings of the 22nd IFAC World
Congress, Yokohama, Japan, pp. 6666-6671, July 2023.
Abstract:
Piecewise-affine (PWA) approximations are widely used among hybrid
modeling frameworks as a way to increase computational efficiency in
nonlinear control and optimization problems. A variety of approaches
to construct PWA approximations have been proposed, most of which are
tailored to specific application areas by using some prior knowledge
of the system in their assumptions and/or steps. In this paper, a
parametric method is proposed to identify PWA approximations of
nonlinear systems, without any prior knowledge of their dynamics or
application requirements. The algorithm defines the regions
parametrically using hyperplanes to cut the domain, and increases the
number of regions iteratively until a user-defined error tolerance
criterion is met. General remarks are given on the algorithm's
implementation and a case study is provided to illustrate its
application to vehicle dynamics.