Robust Invariant Set Analysis of Boolean Networks
In this paper, the robust invariant set (RIS) of Boolean (control) networks with disturbances is investigated. First, for a given fixed point, consider a special set called immediate neighborhoods of the fixed point; then a discrete derivative of Boolean functions at the fixed point is used to analy...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/2731395 |
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| _version_ | 1832561032190492672 |
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| author | Bowen Li Jungang Lou Yang Liu Zhen Wang |
| author_facet | Bowen Li Jungang Lou Yang Liu Zhen Wang |
| author_sort | Bowen Li |
| collection | DOAJ |
| description | In this paper, the robust invariant set (RIS) of Boolean (control) networks with disturbances is investigated. First, for a given fixed point, consider a special set called immediate neighborhoods of the fixed point; then a discrete derivative of Boolean functions at the fixed point is used to analyze the robust invariance, based on which a sufficient condition is obtained. Second, for more general sets, the robust output control invariant set (ROCIS) of Boolean control networks (BCNs) is investigated by semitensor product (STP) of matrices. Then, under a given output feedback controller, we obtain a necessary and sufficient condition to check whether a given set is robust control invariant set (RCIS). Furthermore, output feedback controllers are designed to make a set to be a RCIS. Finally, the proposed methods are illustrated by a reduced model of the lac operon in E. coli. |
| format | Article |
| id | doaj-art-992ab7333d834128a6030fd5c6b81f1c |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-992ab7333d834128a6030fd5c6b81f1c2025-02-03T01:26:14ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/27313952731395Robust Invariant Set Analysis of Boolean NetworksBowen Li0Jungang Lou1Yang Liu2Zhen Wang3College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaSchool of Information Engineering, Huzhou University, Huzhou 313000, ChinaCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaIn this paper, the robust invariant set (RIS) of Boolean (control) networks with disturbances is investigated. First, for a given fixed point, consider a special set called immediate neighborhoods of the fixed point; then a discrete derivative of Boolean functions at the fixed point is used to analyze the robust invariance, based on which a sufficient condition is obtained. Second, for more general sets, the robust output control invariant set (ROCIS) of Boolean control networks (BCNs) is investigated by semitensor product (STP) of matrices. Then, under a given output feedback controller, we obtain a necessary and sufficient condition to check whether a given set is robust control invariant set (RCIS). Furthermore, output feedback controllers are designed to make a set to be a RCIS. Finally, the proposed methods are illustrated by a reduced model of the lac operon in E. coli.http://dx.doi.org/10.1155/2019/2731395 |
| spellingShingle | Bowen Li Jungang Lou Yang Liu Zhen Wang Robust Invariant Set Analysis of Boolean Networks Complexity |
| title | Robust Invariant Set Analysis of Boolean Networks |
| title_full | Robust Invariant Set Analysis of Boolean Networks |
| title_fullStr | Robust Invariant Set Analysis of Boolean Networks |
| title_full_unstemmed | Robust Invariant Set Analysis of Boolean Networks |
| title_short | Robust Invariant Set Analysis of Boolean Networks |
| title_sort | robust invariant set analysis of boolean networks |
| url | http://dx.doi.org/10.1155/2019/2731395 |
| work_keys_str_mv | AT bowenli robustinvariantsetanalysisofbooleannetworks AT junganglou robustinvariantsetanalysisofbooleannetworks AT yangliu robustinvariantsetanalysisofbooleannetworks AT zhenwang robustinvariantsetanalysisofbooleannetworks |