Bisimilarity Enforcement for Discrete Event Systems Using Deterministic Control

The supervisory control theory of fuzzy discrete event systems (FDESs) for fuzzy language equivalence has been developed. However, in a way, language equivalence has limited expressiveness. So if the given specification can not be expressed by language equivalence, then the control for language equivalence does not work. In this paper, we further establish the supervisory control theory of FDESs for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence. First, we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two FDESs. Then we present a method for deciding whether there is a fuzzy simulation or not. In addition, we also show several basic properties of fuzzy simulation relations. Afterwards, we put forward the notion of fuzzy simulation-based controllability, and particularly show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of FDESs. Moreover, we study the "range" control problem of FDESs. Some examples are given to illustrate the main results obtained.Index Terms-fuzzy discrete event systems (FDESs), supervisory control, fuzzy simulation equivalence, simulation-based controllability, fuzzy finite automata. Daowen Qiu received the M.S. degree in mathematics in 1993 from Jiangxi

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“…Firstly, we introduce the following two notions for finite automata, which have been presented in [37], [6].…”

Section: A Fuzzy Simulation and Fuzzy Simulation Equivalencementioning

confidence: 99%

Supervisory Control of Fuzzy Discrete-Event Systems for Simulation Equivalence

Deng

Qiu

2015

IEEE Trans. Fuzzy Syst.

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“…Various supervisory control problems for nondeterministic systems were studied in [2]- [10]. In particular, a general case that both the plant and the specification are nondeterministic, and a supervisor is allowed to be nondeterministic was considered in [2], [9].…”

Section: Introductionmentioning

confidence: 99%

“…The small model theorem was generalized to the setting of partial event observation in [12]. To reduce the computational complexity for verifying the existence of a supervisor, a special case that a supervisor is deterministic was considered in [10]. It was shown that, in this special case, the complexity for verifying the existence of a bisimilarity enforcing deterministic supervisor is linear in the size of the plant and singly exponential in the size of the specification.…”

Section: Introductionmentioning

confidence: 99%

Bisimilarity Control of Nondeterministic Discrete Event Systems under Event and State Observations

Kimura

Takai

2014

IEICE Trans. Inf. & Syst.

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Katsuyuki KIMURA†a) , Nonmember and Shigemasa TAKAI †b) , Member SUMMARYIn this paper, we study a supervisory control problem for plants and specifications modeled by nondeterministic automata. This problem requires to synthesize a nondeterministic supervisor such that the supervised plant is bisimilar to a given specification. We assume that a supervisor can observe not only the event occurrence but also the current state of the plant, and introduce a notion of completeness of a supervisor which guarantees that all nondeterministic transitions caused by events enabled by the supervisor are defined in the supervised plant. We define a notion of partial bisimulation between a given specification and the plant, and prove that it serves as a necessary and sufficient condition for the existence of a bisimilarity enforcing complete supervisor. key words: discrete event system, supervisory control, nondeterministic system, bisimilarity control

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“…In both these works, the existence of a bisimilarity supervisor depends on the existence of a state controllable automaton, which is hard to calculate in a systematic way, and the complexity of checking the existence condition is doubly exponential. To reduce the computational complexity, Zhou & Kumar (2011) specialized to deterministic supervisors. The existence condition for a deterministic bisimilarity supervisor considering nondeterministic plants and nondeterministic specifications was identified.…”

Section: Introductionmentioning

confidence: 99%

“…First, a novel notion of synchronous simulation-based controllability is introduced as a necessary and sufficient condition for the existence of a bisimilarity enforcing supervisor. Although it is equivalent to the conditions in (Zhou & Kumar, 2011) specialized to deterministic specifications, it provides a great insight into what characters should a deterministic specification possesses for bisimilarity control. Second, a test algorithm is proposed to verify the existence condition, which is shown to be polynomial complexity (less than the complexity of the conditions in (Zhou & Kumar, 2011)).…”

Section: Introductionmentioning

confidence: 99%

Bisimilarity enforcing supervisory control for deterministic specifications

2014

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This paper investigates the supervisory control of nondeterministic discrete event systems to enforce bisimilarity with respect to deterministic specifications. A notion of synchronous simulation-based controllability is introduced as a necessary and sufficient condition for the existence of a bisimilarity enforcing supervisor, and a polynomial algorithm is developed to verify such a condition. When the existence condition holds, a supervisor achieving bisimulation equivalence is constructed. Furthermore, when the existence condition does not hold, two different methods are provided for synthesizing maximal permissive sub-specifications.

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Bisimilarity Enforcement for Discrete Event Systems Using Deterministic Control

Cited by 23 publications

References 11 publications

Supervisory Control of Fuzzy Discrete-Event Systems for Simulation Equivalence

Supervisory Control of Fuzzy Discrete-Event Systems for Simulation Equivalence

Bisimilarity Control of Nondeterministic Discrete Event Systems under Event and State Observations

Bisimilarity enforcing supervisory control for deterministic specifications

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