Probabilistic Testing for Stochastic Hybrid Systems

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reachability analysis
stochastic systems
probabilistic safety property
probabilistic testing
reachability property
robust neighborhood concept
stochastic bisimulation function
stochastic hybrid system
testing based method
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In this paper we propose a testing based method for safety/ reachability analysis of stochastic hybrid systems. Testing based methods are characterized by analysis based on the execution traces of the system or the simulation thereof. Testing based method is very appealing because of the simplicity of its execution, the possibility of having a partial verification, and its highly parallel structure. The key idea in this paper is the construction of a robust neighborhood consisting of states that have the same probabilistic safety/reachability properties. We construct the robust neighborhood using the level sets of a stochastic bisimulation function. We also show how to construct stochastic bisimulation functions for systems whose continuous dynamics is stable and linear. As a case example, we consider the problem of conflict detection of aircraft flight, and show that we can infer some robust probabilistic safety property by using the algorithm that we present in this paper.

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Copyright 2008 IEEE. Reprinted from: Julius, A.A.; Pappas, G.J., "Probabilistic testing for stochastic hybrid systems," Decision and Control, 2008. CDC 2008. 47th IEEE Conference on , vol., no., pp.4030-4035, 9-11 Dec. 2008 URL: This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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