2009 Fiscal Year Final Research Report
On Algebraic Behavioral Analyses of Hybrid Petri Nets
| Project/Area Number |
19560409
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
System engineering
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| Research Institution | Fukui University of Technology |
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Principal Investigator |
MATSUMOTO Tadashi Fukui University of Technology, 工学部, 教授 (40020193)
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| Research Collaborator |
OSOGAMI Masahiro 福井工業大学, 工学部, 準教授 (70298389)
MORO Seiichirou 福井大学, 大学院・工学研究科, 準教授 (00303363)
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| Project Period (FY) |
2007 – 2009
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| Keywords | システム工学 / 制御工学 / 数理工学 / ハイブリッドシステム / ペトリネット / 可到達性解析 / 状態方程式 / インバリアント |
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| Research Abstract |
A hybrid Petri net containing both discrete and continuous variables is constructed by discrete Petri nets and continuous Petri nets. Comparison with discrete Petri nets, behaviors of both continuous Petri nets and hybrid Petri nets are very complex and have not been analyzed enough from algebraic approach. In this study, first, a state equation for discrete Petri nets is considered, in which the difference between a destination state and an initial state is fixed, and an arbitrary firing count vector (i.e., a nonnegative integer solution) is completely expressed by elementary T-invariants and fundamental particular solutions. Reachability determination from an initial state to a destination state is algebraically proposed in the bounded space and within finite procedures. Secondly, algebraic analytical approaches of discrete Petri nets are applied to continuous Petri nets and hybrid Petri nets and conditions for applicability to those nets are shown. Thirdly, a novel method for obtaining a discrete system containing only discrete variables from a continuous system with only continuous variables.
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