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Computational Methods for Verification of Stochastic Hybrid Systems (2008)
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| Venue: | IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS - PART A |
| Citations: | 14 - 5 self |
BibTeX
@ARTICLE{Koutsoukos08computationalmethods,
author = {Xenofon D. Koutsoukos and Derek Riley},
title = {Computational Methods for Verification of Stochastic Hybrid Systems},
journal = {IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS - PART A},
year = {2008},
volume = {38},
number = {2}
}
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Abstract
Stochastic hybrid system (SHS) models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing sound computational methods for verification is challenging because of the interaction between the discrete and the continuous stochastic dynamics. In this paper, we propose a probabilistic method for verification of SHSs based on discrete approximations focusing on reachability and safety problems. We show that reachability and safety can be characterized as a viscosity solution of a system of coupled Hamilton–Jacobi–Bellman equations. We present a numerical algorithm for computing the solution based on discrete approximations that are derived using finite-difference methods. An advantage of the method is that the solution converges to the one for the original system as the discretization becomes finer. We also prove that the algorithm is polynomial in the number of states of the discrete approximation. Finally, we illustrate the approach with two benchmarks: a navigation and a room heater example, which have been proposed for hybrid system verification.
Keyphrases
stochastic hybrid system discrete approximation computational method probabilistic method finite-difference method hamilton jacobi bellman equation numerical algorithm critical problem room heater example viscosity solution original system sound computational method continuous stochastic dynamic hybrid system verification reachability property safety problem
