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Polynomial Stochastic Hybrid Systems

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Hybrid Systems: Computation and Control (HSCC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3414))

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Abstract

This paper deals with polynomial stochastic hybrid systems (pSHSs), which generally correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. For pSHSs, the dynamics of the statistical moments of the continuous states evolve according to infinite-dimensional linear ordinary differential equations (ODEs). We show that these ODEs can be approximated by finite-dimensional nonlinear ODEs with arbitrary precision. Based on this result, we provide a procedure to build this type of approximations for certain classes of pSHSs. We apply this procedure for several examples of pSHSs and evaluate the accuracy of the results obtained through comparisons with Monte Carlo simulations. These examples include: the modeling of TCP congestion control both for long-lived and on-off flows; state-estimation for networked control systems; and the stochastic modeling of chemical reactions.

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References

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Author information

Authors and Affiliations

  1. Center for Control Engineering and Computation, University of California, Santa Barbara, CA, 93101

    João Pedro Hespanha

Authors
  1. João Pedro Hespanha
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Editor information

Editors and Affiliations

  1. Automatic Control Laboratory, ETH Zurich, 8092, Zurich, Switzerland

    Manfred Morari

  2. Computer Engineering and Networks Laboratory, ETH Zurich, Switzerland

    Lothar Thiele

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© 2005 Springer-Verlag Berlin Heidelberg

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Hespanha, J.P. (2005). Polynomial Stochastic Hybrid Systems. In: Morari, M., Thiele, L. (eds) Hybrid Systems: Computation and Control. HSCC 2005. Lecture Notes in Computer Science, vol 3414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31954-2_21

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  • DOI: https://doi.org/10.1007/978-3-540-31954-2_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25108-8

  • Online ISBN: 978-3-540-31954-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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