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Lebesgue piecewise affine approximation of nonlinear systems

✍ Scribed by Shun-ichi Azuma; Jun-ichi Imura; Toshiharu Sugie

Publisher
Elsevier
Year
2010
Tongue
English
Weight
997 KB
Volume
4
Category
Article
ISSN
1751-570X

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✦ Synopsis

This paper addresses a piecewise affine (PWA) approximation problem, i.e., a problem of finding a PWA system model which approximates a given nonlinear system. First, we propose a new class of PWA systems, called the Lebesgue PWA approximation systems, as a model to approximate nonlinear systems. Next, we derive an error bound of the PWA approximation model, and provide a technique for constructing the approximation model with specified accuracy. Finally, the proposed method is applied to a gene regulatory network with nonlinear dynamics, which shows that the method is a useful approximation tool.

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✍ BoΕ‘tjan Pregelj; Samo GerkΕ‘ič πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 401 KB

The recently developed methods of explicit (multi-parametric) model predictive control (e-MPC) for hybrid systems provide an interesting opportunity for solving a class of nonlinear control problems. With this approach, the nonlinear process is approximated by a piecewise affine (PWA) hybrid model c