Abstract | ||
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In this chapter we introduce the automata framework CPDP, which stands for Communicating Piecewise Deterministic Markov Processes. CPDP is developed for compositional modelling and analysis for a class of stochastic hybrid systems. We define a parallel composition operator, denoted as vertical bar(P)(A)vertical bar, for CPDPs, which can be used to interconnect component-CPDPs, to form the composite system (which consists of all components, interacting with each other). We show that the result of composing CPDPs with vertical bar(P)(A)vertical bar is again a CPDP (i.e., the class of CPDPs is closed under vertical bar(P)(A)vertical bar). Under certain conditions, the evolution of the state of a CPDP can be modelled as a stochastic process. We show that for these CPDPs, this stochastic process can always be modelled as a PDP (Piecewise Deterministic Markov Process) and we present an algorithm that finds the corresponding PDP of a CPDP. After that, we present an extended CPDP framework called value-passing CPDP. This framework provides richer interaction possibilities, where components can communicate information about their continuous states to each other. We give an Air Traffic Management example, modelled as a value-passing CPDP and we show that according to the algorithm, this CPDP behavior can be modelled as a PDP. Finally, we define bisimulation relations for CPDPs. We prove that bisimilar CPDPs exhibit equal stochastic behavior. Bisimulation can be used as a state reduction technique by substituting a CPDP (or a CPDP component) by a bisimulation-equivalent CPDP (or CPDP component) with a smaller state space. This can be done because we know that such a substitution will not change the stochastic behavior. |
Year | DOI | Venue |
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2003 | 10.1007/11587392_3 | LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES |
Keywords | Field | DocType |
state space,stochastic process | Mathematical optimization,Markov process,Automaton,Piecewise-deterministic Markov process,Stochastic process,Bisimulation,Hybrid system,State space,Piecewise,Mathematics | Conference |
Volume | ISSN | Citations |
337 | 0170-8643 | 11 |
PageRank | References | Authors |
1.27 | 3 | 3 |
Name | Order | Citations | PageRank |
---|---|---|---|
stefan strubbe | 1 | 22 | 2.87 |
A. Agung Julius | 2 | 396 | 43.88 |
arjan van der schaft | 3 | 992 | 138.91 |