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

11 Citations (Scopus)

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages76-89
Number of pages14
Volume4416 LNCS
StatePublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Reachability Analysis
Affine Systems
Biological systems
Lactose
Reachability
Hybrid systems
Biological Systems
Hybrid Systems
Quorum Sensing
Ants
Glucose
Reachable Set
Invariant
Bistability
Rectangle
Convexity
Vector Field
Proof by induction
Calculate
Demonstrate

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Berman, S., Halász, Á., & Kumar, V. (2007). MARCO: A reachability algorithm for multi-affine systems with applications to biological systems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4416 LNCS, pp. 76-89). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4416 LNCS).

MARCO : A reachability algorithm for multi-affine systems with applications to biological systems. / Berman, Spring; Halász, Ádám; Kumar, Vijay.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4416 LNCS 2007. p. 76-89 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4416 LNCS).

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

Berman, S, Halász, Á & Kumar, V 2007, MARCO: A reachability algorithm for multi-affine systems with applications to biological systems. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4416 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4416 LNCS, pp. 76-89, 10th International Conference on Hybrid Systems: Computation and Control, HSCC 2007, Pisa, Italy, 4/3/07.
Berman S, Halász Á, Kumar V. MARCO: A reachability algorithm for multi-affine systems with applications to biological systems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4416 LNCS. 2007. p. 76-89. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Berman, Spring ; Halász, Ádám ; Kumar, Vijay. / MARCO : A reachability algorithm for multi-affine systems with applications to biological systems. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4416 LNCS 2007. pp. 76-89 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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