On equivalence notions for discrete-time stochastic control systems

Giordano Pola, Costanzo Manes, Arjan J. van der Schaft, Maria Domenica Di Benedetto

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5 Citations (Scopus)


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 nonlinear control systems with possibly degenerate distributed disturbances. The notions are inspired by the analogue notions that exist for probabilistic chains and for behavioral systems, respectively. Connections between the two notions and also with stochastic reachability are discussed. For the subclass of discrete-time stochastic linear control systems with multivariate possibly degenerate normal distributed disturbances, geometric necessary and sufficient conditions for checking stochastic bisimulation equivalence and stochastic external behavior equivalence are derived. The proposed results nicely extend the theory of bisimulation equivalence and equivalence of external behavior known for non-deterministic control systems to a stochastic setting.
Original languageEnglish
Number of pages6
Publication statusPublished - 2015
Event54th IEEE Conference on Decision and Control (CDC) - Osaka, Japan
Duration: 15-Dec-201518-Dec-2015


Conference54th IEEE Conference on Decision and Control (CDC)

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