Approximate Abstractions of Stochastic Hybrid Systems
We present a constructive procedure for obtaining a finite approximate abstraction of a discrete-time stochastic hybrid system. The procedure consists of a partition of the state space of the system and depends on a controllable parameter. Given proper continuity assumptions on the model, the approx...
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| Veröffentlicht in: | IEEE transactions on automatic control 2011-11, Vol.56 (11), p.2688-2694 |
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| container_title | IEEE transactions on automatic control |
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| creator | Abate, A. D'Innocenzo, A. Di Benedetto, M. D. |
| description | We present a constructive procedure for obtaining a finite approximate abstraction of a discrete-time stochastic hybrid system. The procedure consists of a partition of the state space of the system and depends on a controllable parameter. Given proper continuity assumptions on the model, the approximation errors introduced by the abstraction procedure are explicitly computed and it is shown that they can be tuned through the parameter of the partition. The abstraction is interpreted as a Markov set-Chain. We show that the enforcement of certain ergodic properties on the stochastic hybrid model implies the existence of a finite abstraction with finite error in time over the concrete model, and allows introducing a finite-time algorithm that computes the abstraction. |
| doi_str_mv | 10.1109/TAC.2011.2160595 |
| format | Article |
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D.</creatorcontrib><title>Approximate Abstractions of Stochastic Hybrid Systems</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>We present a constructive procedure for obtaining a finite approximate abstraction of a discrete-time stochastic hybrid system. The procedure consists of a partition of the state space of the system and depends on a controllable parameter. Given proper continuity assumptions on the model, the approximation errors introduced by the abstraction procedure are explicitly computed and it is shown that they can be tuned through the parameter of the partition. The abstraction is interpreted as a Markov set-Chain. 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D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Approximate Abstractions of Stochastic Hybrid Systems</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2011-11-01</date><risdate>2011</risdate><volume>56</volume><issue>11</issue><spage>2688</spage><epage>2694</epage><pages>2688-2694</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>We present a constructive procedure for obtaining a finite approximate abstraction of a discrete-time stochastic hybrid system. The procedure consists of a partition of the state space of the system and depends on a controllable parameter. Given proper continuity assumptions on the model, the approximation errors introduced by the abstraction procedure are explicitly computed and it is shown that they can be tuned through the parameter of the partition. The abstraction is interpreted as a Markov set-Chain. 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| subjects | Algorithms Approximation Approximation methods Computational modeling Ergodic processes Exact sciences and technology Fluctuation phenomena, random processes, noise, and brownian motion Hybrid systems Kernel Markov Chains Markov processes Mathematical analysis Mathematical models Mathematics Partitions Physics Probabilistic logic Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Statistical physics, thermodynamics, and nonlinear dynamical systems Steady-state stochastic hybrid systems Stochasticity |
| title | Approximate Abstractions of Stochastic Hybrid Systems |
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