Communicating Piecewise Deterministic Markov Processes

Strubbe, Stefan; Schaft, van der Arjan; Blom, H.A.P.; Lygeros, John

doi:10.1007/11587392_3

Cited by 11 publications

(33 citation statements)

References 5 publications

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“…Since the definition given in [4] generalizes the one given in [23] for probabilistic chains, then both Definition 3.3 and the one given in [7], are in fact based on the same ideas given in the seminal work [23]. Regarding the comparison with the definitions of stochastic bisimulation given in [38,39] for CPDMP, we recall that the semantic of CPDMP is characterized by no stochasticity in the continuous-state flow; stochasticity only appears in the discrete-state dynamics, via spontaneous Poisson-type transitions and in the reset of both continuous and discrete variables. Since the systems in (3.1) present stochasticity in the continuous-state flow and have no discrete-state dynamics, Definition 3.3 and the one given in [38,39] are not comparable.…”

Section: Equivalence Notionsmentioning

confidence: 98%

“…Remark 3.4. As stressed in the introduction, this paper is within the research line (D2)-(R3)-(E1), where notions of stochastic bisimulation have been also proposed for General Stochastic Hybrid Systems (GSHS) with no inputs and outputs in [7] and, for Communicating Piecewise Deterministic Markov Processes (CPDMP) in [38,39]. A comparison of the proposed Definition 3.3 with the ones given in [7] and [38,39] follows.…”

Section: Equivalence Notionsmentioning

confidence: 99%

“…As stressed in the introduction, this paper is within the research line (D2)-(R3)-(E1), where notions of stochastic bisimulation have been also proposed for General Stochastic Hybrid Systems (GSHS) with no inputs and outputs in [7] and, for Communicating Piecewise Deterministic Markov Processes (CPDMP) in [38,39]. A comparison of the proposed Definition 3.3 with the ones given in [7] and [38,39] follows. Although the mathematical tools employed in [7] are based on Category Theory and hence, different from the ones utilized in the present paper, the notion proposed in [7] in fact generalizes the one of stochastic bisimulation given for Labelled Markov Processes with countable sets of states in [4] to GSHS.…”

Section: Equivalence Notionsmentioning

confidence: 99%

“…Regarding the comparison with the definitions of stochastic bisimulation given in [38,39] for CPDMP, we recall that the semantic of CPDMP is characterized by no stochasticity in the continuous-state flow; stochasticity only appears in the discrete-state dynamics, via spontaneous Poisson-type transitions and in the reset of both continuous and discrete variables. Since the systems in (3.1) present stochasticity in the continuous-state flow and have no discrete-state dynamics, Definition 3.3 and the one given in [38,39] are not comparable. However, we mention that the definitions proposed in [38,39] are inspired by the one given in [18] for Interactive Markov Chains which combines the classical definition of bisimulation for concurrent (non-stochastic) processes (see e.g.…”

Section: Equivalence Notionsmentioning

confidence: 99%

“…Within the research line (D2)-(R3)-(E1) where the present paper is placed, a notion of bisimulation for general stochastic hybrid systems (with no inputs and outputs) has been proposed in [7] and for communicating piecewise deterministic markov processes in [38,39]. However, given the generality of the models considered in [7,38,39], checkable…”

Section: Introductionmentioning

confidence: 99%

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On equivalence notions for discrete-time stochastic control systems

Pola

Manes

Schaft

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

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In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic linear control systems with possibly degenerate normally distributed disturbances. The first notion is inspired by the notion of probabilistic bisimulation for probabilistic chains while the second one by the notion of equivalence of external behavior for (nonstochastic) behavioral systems. Geometric necessary and sufficient conditions for checking these notions are derived. Model reduction via Kalman-like decomposition is also proposed. Connections with stochastic linear realization theory and stochastic reachability are established.

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Section: Equivalence Notionsmentioning

confidence: 98%

Section: Equivalence Notionsmentioning

confidence: 99%

Section: Equivalence Notionsmentioning

confidence: 99%

Section: Equivalence Notionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On equivalence notions for discrete-time stochastic control systems

Pola

Manes

Schaft

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Bisimulation for Communicating Piecewise Deterministic Markov Processes (CPDPs)

Strubbe

Schaft

2005

Hybrid Systems: Computation and Control

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CPDPs (Communicating Piecewise Deterministic Markov Processes) can be used for compositional specification of systems from the class of stochastic hybrid processes formed by PDPs (Piecewise Deterministic Markov Processes). We define CPDPs and the composition of CPDPs, and prove that the class of CPDPs is closed under composition. Then we introduce a notion of bisimulation for PDPs and CPDPs and we prove that bisimilar PDPs as well as bisimilar CPDPs have equal stochastic behavior. Finally, as main result, we prove the congruence property that, for a composite CPDP, substituting components by different but bisimilar components results in a CPDP that is bisimilar to the original composite CPDP (and therefore has equal stochastic behavior).

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