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Approximate model checking of stochastic hybrid systems , J.-P. Katoen

Summary: Approximate model checking of stochastic hybrid systems
A. Abate
, J.-P. Katoen
, J. Lygeros
, and M. Prandini§
A method for approximate model checking of stochastic hybrid systems with provable approximation
guarantees is proposed. We focus on the probabilistic invariance problem for discrete time stochastic hybrid
systems and propose a two-step scheme. The stochastic hybrid system is first approximated by a finite state
Markov chain. The approximating chain is then model checked for probabilistic invariance. Under certain
regularity conditions on the transition and reset kernels governing the dynamics of the stochastic hybrid
system, the invariance probability computed using the approximating Markov chain is shown to converge
to the invariance probability of the original stochastic hybrid system, as the grid used in the approximation
gets finer. A bound on the convergence rate is also provided. The performance of the two-step approximate
model checking procedure is assessed on a case study of a multi-room heating system.
1 Introduction
Stochastic hybrid systems are a broad and widely applicable class of dynamical systems that involve the
interaction of discrete, continuous, and probabilistic dynamics. Because of their generality, stochastic hybrid
systems have found applications in many areas, including telecommunication networks, manufacturing systems,
transportation, and biological systems (see, for example, [10, 13] for an overview). The importance of stochastic


Source: Abate, Alessandro - Faculty of Mechanical, Maritime and Materials Engineering, Technische Universiteit Delft


Collections: Engineering