State estimation for delayed genetic regulatory networks based on passivity theory
•This paper is concerned with the state estimation problem for delayed genetic regulatory networks based on passivity theory.•The main purpose is to design the state estimator to approximate the true concentrations of the mRNA and protein through measurement outputs.•Time-varying delays are explicit...
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| Veröffentlicht in: | Mathematical biosciences 2013-08, Vol.244 (2), p.165-175 |
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| creator | Vembarasan, V. Nagamani, G. Balasubramaniam, P. Park, Ju H. |
| description | •This paper is concerned with the state estimation problem for delayed genetic regulatory networks based on passivity theory.•The main purpose is to design the state estimator to approximate the true concentrations of the mRNA and protein through measurement outputs.•Time-varying delays are explicitly assumed to be non-differentiable and the constraint on the delay is removed.•A novel delay-dependent passivity criterion is established for GRNs.
This paper is concerned with the state estimation problem for delayed genetic regulatory networks (GRNs) based on passivity analysis approach. The main purpose of the problem is to design the estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. Time-varying delays are explicitly assumed to be non-differentiable and constraint on the derivative of the time-varying delay is less than one can be removed. Based on the Lyapunov–Krasovskii functionals involving triple integral terms, using some integral inequalities and convex combination technique, a delay-dependent passivity criterion is established for GRNs in terms of linear matrix inequalities (LMIs) that can efficiently be solved by any available LMI solvers. Finally, numerical examples and simulation are presented to demonstrate the efficiency of the proposed estimation schemes. |
| doi_str_mv | 10.1016/j.mbs.2013.05.003 |
| format | Article |
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This paper is concerned with the state estimation problem for delayed genetic regulatory networks (GRNs) based on passivity analysis approach. The main purpose of the problem is to design the estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. Time-varying delays are explicitly assumed to be non-differentiable and constraint on the derivative of the time-varying delay is less than one can be removed. Based on the Lyapunov–Krasovskii functionals involving triple integral terms, using some integral inequalities and convex combination technique, a delay-dependent passivity criterion is established for GRNs in terms of linear matrix inequalities (LMIs) that can efficiently be solved by any available LMI solvers. Finally, numerical examples and simulation are presented to demonstrate the efficiency of the proposed estimation schemes.</description><identifier>ISSN: 0025-5564</identifier><identifier>EISSN: 1879-3134</identifier><identifier>DOI: 10.1016/j.mbs.2013.05.003</identifier><identifier>PMID: 23707485</identifier><language>eng</language><publisher>United States: Elsevier Inc</publisher><subject>Combinatorial Chemistry Techniques - statistics & numerical data ; Computer Simulation - statistics & numerical data ; Gene Regulatory Networks - genetics ; Genetic regulatory networks ; Lyapunov–Krasovskii functionals ; Models, Genetic ; Passivity theory ; RNA, Messenger - biosynthesis ; RNA, Messenger - chemistry ; RNA, Messenger - genetics ; State estimation ; Time Factors</subject><ispartof>Mathematical biosciences, 2013-08, Vol.244 (2), p.165-175</ispartof><rights>2013 Elsevier Inc.</rights><rights>Copyright © 2013 Elsevier Inc. All rights reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c386t-645beb746401cf12fdd3007a19ab43b39ca8a4846b10b11973aa27d28b86365a3</citedby><cites>FETCH-LOGICAL-c386t-645beb746401cf12fdd3007a19ab43b39ca8a4846b10b11973aa27d28b86365a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.mbs.2013.05.003$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/23707485$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Vembarasan, V.</creatorcontrib><creatorcontrib>Nagamani, G.</creatorcontrib><creatorcontrib>Balasubramaniam, P.</creatorcontrib><creatorcontrib>Park, Ju H.</creatorcontrib><title>State estimation for delayed genetic regulatory networks based on passivity theory</title><title>Mathematical biosciences</title><addtitle>Math Biosci</addtitle><description>•This paper is concerned with the state estimation problem for delayed genetic regulatory networks based on passivity theory.•The main purpose is to design the state estimator to approximate the true concentrations of the mRNA and protein through measurement outputs.•Time-varying delays are explicitly assumed to be non-differentiable and the constraint on the delay is removed.•A novel delay-dependent passivity criterion is established for GRNs.
This paper is concerned with the state estimation problem for delayed genetic regulatory networks (GRNs) based on passivity analysis approach. The main purpose of the problem is to design the estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. Time-varying delays are explicitly assumed to be non-differentiable and constraint on the derivative of the time-varying delay is less than one can be removed. Based on the Lyapunov–Krasovskii functionals involving triple integral terms, using some integral inequalities and convex combination technique, a delay-dependent passivity criterion is established for GRNs in terms of linear matrix inequalities (LMIs) that can efficiently be solved by any available LMI solvers. Finally, numerical examples and simulation are presented to demonstrate the efficiency of the proposed estimation schemes.</description><subject>Combinatorial Chemistry Techniques - statistics & numerical data</subject><subject>Computer Simulation - statistics & numerical data</subject><subject>Gene Regulatory Networks - genetics</subject><subject>Genetic regulatory networks</subject><subject>Lyapunov–Krasovskii functionals</subject><subject>Models, Genetic</subject><subject>Passivity theory</subject><subject>RNA, Messenger - biosynthesis</subject><subject>RNA, Messenger - chemistry</subject><subject>RNA, Messenger - genetics</subject><subject>State estimation</subject><subject>Time Factors</subject><issn>0025-5564</issn><issn>1879-3134</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqFkM1O3DAURi1EVQboA3RTZckm6b3xX6KuEGoLEhIShbVlOzfgaWYy2B6qeXuMhnZJV5auzvkkH8Y-IzQIqL4um5VLTQvIG5ANAD9gC-x0X3Pk4pAtAFpZS6nEETtOaQmAGlF9ZEct16BFJxfs9le2mSpKOaxsDvO6GudYDTTZHQ3VA60pB19FethONs9xV5XDnzn-TpWzqRBF2NiUwnPIuyo_UkFO2YfRTok-vb0n7P7H97uLy_r65ufVxfl17Xmncq2EdOS0UALQj9iOw8ABtMXeOsEd773trOiEcggOsdfc2lYPbec6xZW0_ISd7Xc3cX7alh-YVUiepsmuad4mg7LM9Upq-D8qSrxet70sKO5RH-eUIo1mE0uauDMI5rW6WZpS3bxWNyBNEYvz5W1-61Y0_DP-Zi7Atz1ApcdzoGiSD7T2NIRIPpthDu_MvwBhBZJX</recordid><startdate>201308</startdate><enddate>201308</enddate><creator>Vembarasan, V.</creator><creator>Nagamani, G.</creator><creator>Balasubramaniam, P.</creator><creator>Park, Ju H.</creator><general>Elsevier Inc</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>7QO</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope><scope>RC3</scope></search><sort><creationdate>201308</creationdate><title>State estimation for delayed genetic regulatory networks based on passivity theory</title><author>Vembarasan, V. ; Nagamani, G. ; Balasubramaniam, P. ; Park, Ju H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c386t-645beb746401cf12fdd3007a19ab43b39ca8a4846b10b11973aa27d28b86365a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Combinatorial Chemistry Techniques - statistics & numerical data</topic><topic>Computer Simulation - statistics & numerical data</topic><topic>Gene Regulatory Networks - genetics</topic><topic>Genetic regulatory networks</topic><topic>Lyapunov–Krasovskii functionals</topic><topic>Models, Genetic</topic><topic>Passivity theory</topic><topic>RNA, Messenger - biosynthesis</topic><topic>RNA, Messenger - chemistry</topic><topic>RNA, Messenger - genetics</topic><topic>State estimation</topic><topic>Time Factors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Vembarasan, V.</creatorcontrib><creatorcontrib>Nagamani, G.</creatorcontrib><creatorcontrib>Balasubramaniam, P.</creatorcontrib><creatorcontrib>Park, Ju H.</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>Biotechnology Research Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>Genetics Abstracts</collection><jtitle>Mathematical biosciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Vembarasan, V.</au><au>Nagamani, G.</au><au>Balasubramaniam, P.</au><au>Park, Ju H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>State estimation for delayed genetic regulatory networks based on passivity theory</atitle><jtitle>Mathematical biosciences</jtitle><addtitle>Math Biosci</addtitle><date>2013-08</date><risdate>2013</risdate><volume>244</volume><issue>2</issue><spage>165</spage><epage>175</epage><pages>165-175</pages><issn>0025-5564</issn><eissn>1879-3134</eissn><abstract>•This paper is concerned with the state estimation problem for delayed genetic regulatory networks based on passivity theory.•The main purpose is to design the state estimator to approximate the true concentrations of the mRNA and protein through measurement outputs.•Time-varying delays are explicitly assumed to be non-differentiable and the constraint on the delay is removed.•A novel delay-dependent passivity criterion is established for GRNs.
This paper is concerned with the state estimation problem for delayed genetic regulatory networks (GRNs) based on passivity analysis approach. The main purpose of the problem is to design the estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. Time-varying delays are explicitly assumed to be non-differentiable and constraint on the derivative of the time-varying delay is less than one can be removed. Based on the Lyapunov–Krasovskii functionals involving triple integral terms, using some integral inequalities and convex combination technique, a delay-dependent passivity criterion is established for GRNs in terms of linear matrix inequalities (LMIs) that can efficiently be solved by any available LMI solvers. Finally, numerical examples and simulation are presented to demonstrate the efficiency of the proposed estimation schemes.</abstract><cop>United States</cop><pub>Elsevier Inc</pub><pmid>23707485</pmid><doi>10.1016/j.mbs.2013.05.003</doi><tpages>11</tpages></addata></record> |
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| subjects | Combinatorial Chemistry Techniques - statistics & numerical data Computer Simulation - statistics & numerical data Gene Regulatory Networks - genetics Genetic regulatory networks Lyapunov–Krasovskii functionals Models, Genetic Passivity theory RNA, Messenger - biosynthesis RNA, Messenger - chemistry RNA, Messenger - genetics State estimation Time Factors |
| title | State estimation for delayed genetic regulatory networks based on passivity theory |
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