Mesh-Based Affine Abstraction of Nonlinear Systems with Tighter Bounds

Kanishka Raj Singh, Qiang Shen, Sze Yong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Scopus citations


In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the over-approximation of its nonlinear dynamics by a pair of piecewise affine functions that 'includes' the dynamical characteristics of the original system. As such, guarantees for controllers or estimators based on the affine abstraction also apply to the original nonlinear system. Our approach consists of solving a linear programming (LP) problem that over-approximates the nonlinear function at only the grid points of a mesh with a given resolution and then accounting for the entire domain via an appropriate correction term. To achieve a desired approximation accuracy, we also iteratively subdivide the domain into subregions. Our method applies to nonlinear functions with different degrees of smoothness, including Lipschitz continuous functions, and improves on existing approaches by enabling the use of tighter bounds. Finally, we compare the effectiveness of our approach with existing optimization-based methods in simulation and illustrate its applicability for estimator design.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781538613955
StatePublished - Jul 2 2018
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference57th IEEE Conference on Decision and Control, CDC 2018
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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