Paper Info
Title
Polynomial stochastic hybrid systems
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.
Year
DOI
Venue
2005
10.1007/978-3-540-31954-2_21
HSCC
Keywords
Field
DocType
monte carlo simulation,polynomial stochastic hybrid system,stochastic modeling,hybrid system,tcp congestion control,continuous state,polynomial continuous vector field,finite-dimensional nonlinear odes,arbitrary precision,networked control system,chemical reaction
Applied mathematics,Monte Carlo method,Mathematical optimization,Nonlinear system,Ordinary differential equation,Polynomial,Vector field,Hybrid system,Ode,Mathematics,Method of moments (statistics)
Conference
Volume
ISSN
ISBN
3414
0302-9743
3-540-25108-1
Citations 
PageRank 
References 
21
6.93
4
Authors
1
Name
Order
Citations
PageRank
João Pedro Hespanha114018.62