Tight Remainder-Form Decomposition Functions With Applications to Constrained Reachability and Guaranteed State Estimation

Mohammad Khajenejad, Sze Zheng Yong

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this article, we propose a tractable family of remainder-form mixed-monotone decomposition functions that are useful for overapproximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a new class of nonsmooth, discontinuous nonlinear systems that we call either-sided locally Lipschitz semicontinuous systems, which we show to be a strict superset of locally Lipschitz continuous systems, thus expanding the set of systems that are formally known to be mixed-monotone. In addition, we derive lower and upper bounds for the overapproximation error and show that the lower bound is achieved with our proposed approach, i.e., our approach constructs the tightest, tractable remainder-form mixed-monotone decomposition function. Moreover, we introduce a set inversion algorithm that along with the proposed decomposition functions can be used for constrained reachability analysis and guaranteed state estimation for continuous- and discrete-time systems with bounded noise.

Original languageEnglish (US)
Pages (from-to)7057-7072
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume68
Issue number12
DOIs
StatePublished - Dec 1 2023
Externally publishedYes

Keywords

  • ELLS systems
  • Nonlinear dynamical systems
  • mixed-monotonicity
  • one-sided decomposition functions
  • reachability analysis

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications

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