{"title":"$K$-Step Opacity Verification and Enforcement of Time Labeled Petri Net Systems","authors":"Yifan Dong;Dimitri Lefebvre;Zhiwu Li","doi":"10.1109/TAC.2025.3552020","DOIUrl":null,"url":null,"abstract":"This article presents a procedure for <inline-formula><tex-math>$K$</tex-math></inline-formula>-step opacity verification and enforcement of timed observations generated from discrete event systems modeled by time labeled Petri nets. Within the framework of a timed discrete event system that is partially observed by an intruder, a <inline-formula><tex-math>$K$</tex-math></inline-formula>-step opaque timed observation means that an intruder has observed the system with time stamps but is not able to deduce the secret information within the knowledge derived from the last <inline-formula><tex-math>$K$</tex-math></inline-formula> steps of the timed observation. We propose an information structure called a partial modified state class graph with respect to a timed observation. Then, based on the particular graph, an algorithm is designed to construct a delayed marking estimator that is used for the verification of <inline-formula><tex-math>$K$</tex-math></inline-formula>-step opacity of a timed observation by solving a number of linear programming problems. Finally, when the timed observation is not <inline-formula><tex-math>$K$</tex-math></inline-formula>-step opaque, a strategy by adjusting the time horizons of transitions with soft time intervals is proposed for the opacity enforcement purpose.","PeriodicalId":13201,"journal":{"name":"IEEE Transactions on Automatic Control","volume":"70 9","pages":"5848-5863"},"PeriodicalIF":7.0000,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Automatic Control","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10930533/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This article presents a procedure for $K$-step opacity verification and enforcement of timed observations generated from discrete event systems modeled by time labeled Petri nets. Within the framework of a timed discrete event system that is partially observed by an intruder, a $K$-step opaque timed observation means that an intruder has observed the system with time stamps but is not able to deduce the secret information within the knowledge derived from the last $K$ steps of the timed observation. We propose an information structure called a partial modified state class graph with respect to a timed observation. Then, based on the particular graph, an algorithm is designed to construct a delayed marking estimator that is used for the verification of $K$-step opacity of a timed observation by solving a number of linear programming problems. Finally, when the timed observation is not $K$-step opaque, a strategy by adjusting the time horizons of transitions with soft time intervals is proposed for the opacity enforcement purpose.
期刊介绍：
In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering. Two types of contributions are regularly considered:
1) Papers: Presentation of significant research, development, or application of control concepts.
2) Technical Notes and Correspondence: Brief technical notes, comments on published areas or established control topics, corrections to papers and notes published in the Transactions.
In addition, special papers (tutorials, surveys, and perspectives on the theory and applications of control systems topics) are solicited.
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