Positive Invariance of Constrained Affine Dynamics and Its Applications to Hybrid Systems and Safety Verification

Simple item page
dc.contributor.authorShen, Jinglai
dc.date.accessioned2024-08-27T20:37:44Z
dc.date.available2024-08-27T20:37:44Z
dc.date.issued2012-01
dc.description.abstractMotivated by long-time dynamic analysis of hybrid systems and safety verification problems, this paper addresses fundamental positive invariance issues of an affine dynamical system on a general polyhedron and their applications. Necessary and sufficient algebraic conditions are established for the existence of a positively invariant set of an affine system on a polyhedron using the tools of lexicographic relation and long-time oscillatory dynamic analysis. A linear program based algorithm is proposed to verify these conditions, and its computational complexity is analyzed. The positive invariance results are applied to obtain an explicit characterization of global switching behaviors of piecewise affine systems. Further, the positive invariance techniques developed in this paper are exploited to show the decidability of safety verification of a class of affine dynamics on semialgebraic sets.
dc.description.sponsorshipThis work was supported in part by the National Science Foundation under Grant ECCS-0900960. Recommended by Associate Editor H. Ishii.
dc.description.urihttps://ieeexplore.ieee.org/document/5750037
dc.format.extent32 pages
dc.genrejournal articles
dc.genrepreprints
dc.identifierdoi:10.13016/m2wuf4-ftek
dc.identifier.citationShen, Jinglai. “Positive Invariance of Constrained Affine Dynamics and Its Applications to Hybrid Systems and Safety Verification.” IEEE Transactions on Automatic Control 57, no. 1 (January 2012): 3–18. https://doi.org/10.1109/TAC.2011.2142570.
dc.identifier.urihttps://doi.org/10.1109/TAC.2011.2142570
dc.identifier.urihttp://hdl.handle.net/11603/35765
dc.language.isoen_US
dc.publisherIEEE
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Mathematics and Statistics Department
dc.rights© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
dc.subjectEigenvalues and eigenfunctions
dc.subjectHeuristic algorithms
dc.subjectIndexes
dc.subjectPiecewise affine system
dc.subjectpositive invariance
dc.subjectSafety
dc.subjectsafety verification
dc.subjectSwitches
dc.subjectTrajectory
dc.subjectVectors
dc.titlePositive Invariance of Constrained Affine Dynamics and Its Applications to Hybrid Systems and Safety Verification
dc.typeText
dcterms.creatorhttps://orcid.org/0000-0003-2172-4182

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
Positive_Invariance_of_Constrained_Affine_Dynamics.pdf
Size:
803.97 KB
Format:
Adobe Portable Document Format
Download

Collections

UMBC Faculty Collection
UMBC Mathematics and Statistics Department