Abstraction based reachability analysis for finite branching stochastic hybrid systems

In this paper, we address the problem of computing the probability of reaching a desired set in a subclass of stochastic hybrid systems, wherein the stochasticity arises from the randomness of the initial distribution of continuous states, and the probabilistic transitions in the underlying finite s...

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Bibliographic Details
Published in:2017 ACM IEEE 8th International Conference on Cyber Physical Systems (ICCPS) pp. 121 - 130
Main Authors: Zhang, Wenji, Prabhakar, Pavithra, Natarajan, Balasubramaniam
Format: Conference Proceeding
Language:English
Published: New York, NY, USA ACM 18.04.2017
Series:ACM Other Conferences
Subjects:
abstraction based analysis
Computational modeling
Cyber-physical systems
generalized probabilistic transition system
infinite state markov chain
Markov processes
Partitioning algorithms
Probabilistic logic
reachability
Reachability analysis
Software and its engineering > Software organization and properties > Software functional properties > Formal methods
stochastic hybrid system
Theory of computation > Logic > Abstraction
Theory of computation > Logic > Automated reasoning
Theory of computation > Logic > Verification by model checking
Theory of computation > Models of computation > Probabilistic computation
generalized probabilistic transition system
abstraction based analysis
infinite state Markov chain
reachability
stochastic hybrid system
ISBN:9781450349659, 145034965X
Online Access:Get full text
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Summary:In this paper, we address the problem of computing the probability of reaching a desired set in a subclass of stochastic hybrid systems, wherein the stochasticity arises from the randomness of the initial distribution of continuous states, and the probabilistic transitions in the underlying finite state Markov chain. In particular, the continuous dynamics is deterministic for each mode and hence, there are finitely many probabilistic successors for a given state. We exploit this property and extend a partition based abstraction technique developed for finite state systems to the stochastic hybrid system setting. We prove the correctness of our algorithm by defining appropriate simulation relations that relate the stochastic hybrid system to a finite state "generalized" probabilistic transition system that we obtain as a result of abstraction. We show that the simulation relation defined provides upper and lower bounds on the probability of reachability. In particular, tighter bounds can be obtained by refining the partition. We apply our algorithm to automatically analyze a smart home application.
ISBN:9781450349659
145034965X
DOI:10.1145/3055004.3055023