MARCO: A reachability algorithm for multi-affine systems with applications to biological systems

Spring Berman, Ádám Halász, Vijay Kumar

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

12 Scopus citations

Abstract

We present a new algorithm for the reachability analysis of multi-affine hybrid systems. In our previous work on reachability analysis and that of our collaborators [1,2,3], we exploited the convexity of multiaffine functions and the fact that the vector field in modes with rectangular invariants is uniquely determined by its values at the rectangle vertices. In this paper, we explicitly calculate conical overapproximations of the reachable set in the invariant of each mode. We describe our MultiAffine Reachability analysis using Conical Overapproximations, MARCO, and show that it yields results that are superior to those obtained by existing methods for multi-affine hybrid systems. Finally, we demonstrate the application of MARCO to the analysis of an ant house hunting model that incorporates quorum sensing [4] and the analysis of bi-stability of the lactose induction system regulated by glucose and lactose [5].

Original languageEnglish (US)
Title of host publicationHybrid Systems
Subtitle of host publicationComputation and Control - 10th International Conference, HSCC 2007, Proceedings
PublisherSpringer Verlag
Pages76-89
Number of pages14
ISBN (Print)9783540714927
DOIs
StatePublished - Jan 1 2007
Externally publishedYes
Event10th International Conference on Hybrid Systems: Computation and Control, HSCC 2007 - Pisa, Italy
Duration: Apr 3 2007Apr 5 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4416 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Conference on Hybrid Systems: Computation and Control, HSCC 2007
CountryItaly
CityPisa
Period4/3/074/5/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Berman, S., Halász, Á., & Kumar, V. (2007). MARCO: A reachability algorithm for multi-affine systems with applications to biological systems. In Hybrid Systems: Computation and Control - 10th International Conference, HSCC 2007, Proceedings (pp. 76-89). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4416 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-71493-4_9