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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| Published in: | 2017 ACM IEEE 8th International Conference on Cyber Physical Systems (ICCPS) pp. 121 - 130 |
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| Main Authors: | , , |
| Format: | Conference Proceeding |
| Language: | English |
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New York, NY, USA
ACM
18.04.2017
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| ISBN: | 9781450349659, 145034965X |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Prabhakar, Pavithra Natarajan, Balasubramaniam Zhang, Wenji |
| Author_xml | – sequence: 1 givenname: Wenji surname: Zhang fullname: Zhang, Wenji email: wenjizhang@ksu.edu organization: Kansas State University – sequence: 2 givenname: Pavithra surname: Prabhakar fullname: Prabhakar, Pavithra email: pprabhakar@ksu.edu organization: Kansas State University – sequence: 3 givenname: Balasubramaniam surname: Natarajan fullname: Natarajan, Balasubramaniam email: bala@ksu.edu organization: Kansas State University |
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| Keywords | generalized probabilistic transition system abstraction based analysis infinite state Markov chain reachability stochastic hybrid system |
| Language | English |
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| Snippet | 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... |
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| SubjectTerms | 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 |
| Title | Abstraction based reachability analysis for finite branching stochastic hybrid systems |
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