Polynomial stochastic hybrid systems

Authors:
João Pedro Hespanha
Affiliations:
Center for Control Engineering and Computation, University of California, Santa Barbara, CA
Venue:
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Year:
2005

Citing 2
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Journal of Computational Physics

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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.