Bisimulation of dynamical systems

Arjan van der Schaft

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

22 Citations (Scopus)

Abstract

A general notion of bisimulation is studied for dynamical systems. An algebraic characterization of bisimulation together, with an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation of dynamical systems is shown to be a concept which unifies the system-theoretic concepts of state space equivalence and state space reduction, and which allows to study equivalence of systems with non-minimal state space dimension. The notion of bisimulation is especially powerful for 'non-deterministic' dynamical systems, and leads in this case to a notion of equivalence which is finer than equality of external behavior. Furthermore, by merging bisimulation of dynamical systems with bisimulation of concurrent processes a notion of structural bisimulation is developed for hybrid systems with continuous input and output variables.
Original languageUndefined
Title of host publicationHybrid Systems: Computation and Control
EditorsRajeev Alur, George J. Pappas
Place of PublicationBerlin
PublisherSpringer
Pages555-569
Number of pages15
ISBN (Print)978-3-540-21259-1
DOIs
Publication statusPublished - 2004
Event7th International Workshop on Hybrid Systems: Computation and Control, HSCC 2004 - Philadelphia, United States
Duration: 25 Mar 200427 Mar 2004
Conference number: 7

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag
Volume2993
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Workshop

Workshop7th International Workshop on Hybrid Systems: Computation and Control, HSCC 2004
Abbreviated titleHSCC
CountryUnited States
CityPhiladelphia
Period25/03/0427/03/04

Keywords

  • EWI-16805
  • METIS-219892
  • IR-69156

Cite this

van der Schaft, A. (2004). Bisimulation of dynamical systems. In R. Alur, & G. J. Pappas (Eds.), Hybrid Systems: Computation and Control (pp. 555-569). [10.1007/b96398] (Lecture Notes in Computer Science; Vol. 2993). Berlin: Springer. https://doi.org/10.1007/b96398
van der Schaft, Arjan. / Bisimulation of dynamical systems. Hybrid Systems: Computation and Control. editor / Rajeev Alur ; George J. Pappas. Berlin : Springer, 2004. pp. 555-569 (Lecture Notes in Computer Science).
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van der Schaft, A 2004, Bisimulation of dynamical systems. in R Alur & GJ Pappas (eds), Hybrid Systems: Computation and Control., 10.1007/b96398, Lecture Notes in Computer Science, vol. 2993, Springer, Berlin, pp. 555-569, 7th International Workshop on Hybrid Systems: Computation and Control, HSCC 2004, Philadelphia, United States, 25/03/04. https://doi.org/10.1007/b96398

Bisimulation of dynamical systems. / van der Schaft, Arjan.

Hybrid Systems: Computation and Control. ed. / Rajeev Alur; George J. Pappas. Berlin : Springer, 2004. p. 555-569 10.1007/b96398 (Lecture Notes in Computer Science; Vol. 2993).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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N2 - A general notion of bisimulation is studied for dynamical systems. An algebraic characterization of bisimulation together, with an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation of dynamical systems is shown to be a concept which unifies the system-theoretic concepts of state space equivalence and state space reduction, and which allows to study equivalence of systems with non-minimal state space dimension. The notion of bisimulation is especially powerful for 'non-deterministic' dynamical systems, and leads in this case to a notion of equivalence which is finer than equality of external behavior. Furthermore, by merging bisimulation of dynamical systems with bisimulation of concurrent processes a notion of structural bisimulation is developed for hybrid systems with continuous input and output variables.

AB - A general notion of bisimulation is studied for dynamical systems. An algebraic characterization of bisimulation together, with an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation of dynamical systems is shown to be a concept which unifies the system-theoretic concepts of state space equivalence and state space reduction, and which allows to study equivalence of systems with non-minimal state space dimension. The notion of bisimulation is especially powerful for 'non-deterministic' dynamical systems, and leads in this case to a notion of equivalence which is finer than equality of external behavior. Furthermore, by merging bisimulation of dynamical systems with bisimulation of concurrent processes a notion of structural bisimulation is developed for hybrid systems with continuous input and output variables.

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BT - Hybrid Systems: Computation and Control

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van der Schaft A. Bisimulation of dynamical systems. In Alur R, Pappas GJ, editors, Hybrid Systems: Computation and Control. Berlin: Springer. 2004. p. 555-569. 10.1007/b96398. (Lecture Notes in Computer Science). https://doi.org/10.1007/b96398