On the invariance property of reduced supervisors from the perspective of vector discrete-event systems

Jiao, Ting; Chang, Ru; Nan, Xueli

doi:10.1080/00207179.2020.1715485

Cited by 2 publications

(7 citation statements)

References 27 publications

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“…This small manufacturing facility (shown in Figure 7) consists of two classes of components, that is, the supervisor K is obtained. Furthermore, by exploiting symmetry, in Jiao et al [14,15], we show that the reduced counterpart is invariant. Namely, for RN specifications, such as preventing the underflow and overflow of buffers, the reduced version of K, denoted by RK shown in Figure 9, is independent of the numbers of components in each class.…”

Section: Supervisory Control Of Sdes Based On Efficient Relabelingmentioning

confidence: 69%

“…The symmetry of SDES is also exploited in previous works [14][15][16] with a relabeling map 𝜗 : Σ * → T * defined according to…”

Section: Symmetric Discrete-event Systems and Relabelingmentioning

confidence: 99%

“…The symmetry of SDES is also exploited in previous works [14–16] with a relabeling map ϑ : Σ ∗ → T ∗ defined according to

\begin{matrix} alignleft \\ align-1 ϑ (ε) & align-2 = ε; \\ align-1 ϑ (σ) & align-2 \in T_{c} for σ \in Σ_{c}; \\ align-1 ϑ (σ) & align-2 \in T_{u} for σ \in Σ_{u}; \\ align-1 ϑ (s σ) & align-2 = ϑ (s) ϑ (σ) for s \in Σ^{*}, σ \in Σ; \end{matrix}

where T c and T u are the relabeled counterparts of the controllable event subset Σ c and the uncontrollable event subset Σ u , respectively.…”

Section: Preliminariesmentioning

confidence: 99%

“…Thanks to the replicated structures of DES, the reduction in the state space is notable, especially when the degree of symmetry is high. In previous studies [14][15][16], a relabeling map is proposed to exploit the symmetry of DES with replicated structures. The symmetric DES (SDES) therein are composed of several classes of similar components.…”

Section: Introductionmentioning

confidence: 99%

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On efficient relabeling of symmetric discrete‐event systems

Jiao

Bai

2021

Asian Journal of Control

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Symmetric discrete-event systems (SDES) are composed of classes of components with identical structures. By utilizing such symmetry, for specifications irrelevant to the detailed component information, the supervisory control of SDES can be achieved in the relabeled level. Namely, for events fulfilling the same task (similar events) in a class of components, they are relabeled to the same symbol. The relabeling mechanism is first implemented by directly renaming similar events to the same symbol. Then by employing the subset construction algorithm (SCA), the resultant nondeterministic automaton is converted to its deterministic counterpart. As the SCA is computationally intensive, the relabeling algorithm is inefficient, especially when the number of components increases. In this paper, inspired by the construction process of quotient automata, we first employ symmetry to generate the state set of the relabeled automaton. Then the relabeled automaton is generated based on the generated state set and transition information among these states. As we avoid using the SCA to eliminate nondeterminism, the relabeling process is more efficient. A running example is given throughout the paper.

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Section: Supervisory Control Of Sdes Based On Efficient Relabelingmentioning

confidence: 69%

“…The symmetry of SDES is also exploited in previous works [14][15][16] with a relabeling map 𝜗 : Σ * → T * defined according to…”

Section: Symmetric Discrete-event Systems and Relabelingmentioning

confidence: 99%

“…The symmetry of SDES is also exploited in previous works [14–16] with a relabeling map ϑ : Σ ∗ → T ∗ defined according to

\begin{matrix} alignleft \\ align-1 ϑ (ε) & align-2 = ε; \\ align-1 ϑ (σ) & align-2 \in T_{c} for σ \in Σ_{c}; \\ align-1 ϑ (σ) & align-2 \in T_{u} for σ \in Σ_{u}; \\ align-1 ϑ (s σ) & align-2 = ϑ (s) ϑ (σ) for s \in Σ^{*}, σ \in Σ; \end{matrix}

where T c and T u are the relabeled counterparts of the controllable event subset Σ c and the uncontrollable event subset Σ u , respectively.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On efficient relabeling of symmetric discrete‐event systems

Jiao

Bai

2021

Asian Journal of Control

Self Cite

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“…Today, these systems are so complex that intuitive methods are no longer enough to ensure efficient and operational supervision and scheduling. The theory of supervision of DES was developed by Wonham and Ramadge [1,2]. Thanks to formal languages and automata, these authors have introduced concepts like those used in the theory of automatic control of continuous systems.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model for Production Plan Optimization—A Case Study of Discrete Event Systems

et al. 2020

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This paper proposes an optimal scheduling model under production and maintenance constraints for a real case of a discrete event system. The intent was to use the rich mathematical theory and algorithms of optimization in the study of this important class of systems. The current study detailed firstly a new approach for mapping a simulation event relationship graph into a mixed-integer program, with a flexible workshop real case. Several other potential applications of the mathematical model are examined, thanks to the model constraints flexibility characteristics, including a general case of a manufacturing system for optimal resource scheduling, an application on the case of hospital beds’ management. The model extension could be also interesting for other applications like museum systems or the case of big data in complex and social networks.

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On the invariance property of reduced supervisors from the perspective of vector discrete-event systems

Cited by 2 publications

References 27 publications

On efficient relabeling of symmetric discrete‐event systems

On efficient relabeling of symmetric discrete‐event systems

Mathematical Model for Production Plan Optimization—A Case Study of Discrete Event Systems

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