2015 54th IEEE Conference on Decision and Control (CDC) 2015
DOI: 10.1109/cdc.2015.7402371
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On equivalence notions for discrete-time stochastic control systems

Abstract: 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 … Show more

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Cited by 3 publications
(10 citation statements)
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“…The problem addressed in this paper has been recently investigated in the continuous-time domain in [31]; see also [29]. A preliminary version of this paper appeared in the conference publication [32]. The present paper extends the work [32] by introducing novel results on model reduction and finite horizon stochastic safety problems, a discussion on control design via bisimulation and by presenting an application to optimal control for stochastic reachability problems.…”
Section: Introductionmentioning
confidence: 80%
See 4 more Smart Citations
“…The problem addressed in this paper has been recently investigated in the continuous-time domain in [31]; see also [29]. A preliminary version of this paper appeared in the conference publication [32]. The present paper extends the work [32] by introducing novel results on model reduction and finite horizon stochastic safety problems, a discussion on control design via bisimulation and by presenting an application to optimal control for stochastic reachability problems.…”
Section: Introductionmentioning
confidence: 80%
“…A preliminary version of this paper appeared in the conference publication [32]. The present paper extends the work [32] by introducing novel results on model reduction and finite horizon stochastic safety problems, a discussion on control design via bisimulation and by presenting an application to optimal control for stochastic reachability problems. Finally, it also includes proofs of the results proposed.…”
Section: Introductionmentioning
confidence: 81%
See 3 more Smart Citations