Error Bounds for Compositions of Piecewise affine Approximations

Jonah J. Glunt, Jacob A. Siefert, Andrew F. Thompson, Herschel C. Pangborn

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations

Abstract

Nonlinear expressions in dynamic models are often approximated by piecewise affine (PWA) functions to simplify analysis or reduce computational costs. Rather than directly approximating complicated multivariate functions in a high-dimensional space, these can instead be decomposed into a collection of simpler functions, which are then approximated individually and recomposed. This paper provides efficient methods to generate PWA approximations of nonlinear functions via functional decomposition. The key contributions focus on placing breakpoints for PWA approximations to satisfy a desired error tolerance and on bounding the error of PWA compositions as a function of the error tolerance for each component. The proposed methods are used to systematically construct a PWA approximation for a complicated function, either to within a desired error tolerance or to a given level of complexity in the approximation.

Original languageEnglish (US)
Pages (from-to)43-50
Number of pages8
JournalIFAC-PapersOnLine
Volume58
Issue number11
DOIs
StatePublished - Jul 1 2024
Event8th IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2024 - Boulder, United States
Duration: Jul 1 2024Jul 3 2024

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

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