Incremental Affine Abstraction of Nonlinear Systems

Syed M. Hassaan, Mohammad Khajenejad, Spencer Jensen, Qiang Shen, Sze Zheng Yong

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this letter, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes with expanding operating regions. Although the affine abstraction problem can be solved using a single linear program, existing approaches suffer from a computation space complexity that grows exponentially with the state dimension. Thus, the motivation for incremental abstraction is to reduce the space complexity of abstraction algorithms for high-dimensional systems or systems with limited on-board resources. Specifically, we start with an operating region that is a subregion of the state space and compute a pair of affine hyperplanes that bracket the nonlinear function locally. Then, by incrementally expanding the operating region, we dynamically update the two affine hyperplanes such that we eventually yield hyperplanes that are guaranteed to over-approximate the nonlinear system over the entire domain. Finally, the effectiveness of the proposed approach is demonstrated using several numerical examples.

Original languageEnglish (US)
Article number9123441
Pages (from-to)653-658
Number of pages6
JournalIEEE Control Systems Letters
Volume5
Issue number2
DOIs
StatePublished - Apr 2021
Externally publishedYes

Keywords

  • Computational methods
  • large-scale systems
  • model/controller reduction
  • optimization algorithms

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization

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