Parametric Piecewise-Affine Approximation of Nonlinear Systems: A Cut-Based Approach

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.