Approximate Controllability of Semilinear Control System with State Delay Using Tikhonov Regularization
In this paper computation of control for an approximately controllable semilinear system with state delay is studied using Tikhonov regularization. Depending on the state delay occurred in the time interval, approximate controllability of the semilinear control system is proved under the assumption...
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| Veröffentlicht in: | Journal of dynamical and control systems 2024-06, Vol.30 (2), Article 20 |
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| container_title | Journal of dynamical and control systems |
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| creator | Katta, Ravinder Sukavanam, N. |
| description | In this paper computation of control for an approximately controllable semilinear system with state delay is studied using Tikhonov regularization. Depending on the state delay occurred in the time interval, approximate controllability of the semilinear control system is proved under the assumption of approximate controllability of the corresponding linear system without state delay under some assumptions on the system constraints.Computing control for a given target state for the aforesaid system is ill-posed in the sense of Hadamard. Regularized control is computed using Tikhonov regularization for a given target state. Under some assumptions on system and nonlinear function
f
, it is proved that the target state corresponding to the regularized control is very close to the actual state to be attained by the system. Proposed Theory is corroborated with an example of diffusion system. |
| doi_str_mv | 10.1007/s10883-024-09683-3 |
| format | Article |
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f
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f
, it is proved that the target state corresponding to the regularized control is very close to the actual state to be attained by the system. Proposed Theory is corroborated with an example of diffusion system.</description><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Control systems</subject><subject>Controllability</subject><subject>Delay</subject><subject>Dynamical Systems</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Linear systems</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Regularization</subject><subject>Systems Theory</subject><subject>Vibration</subject><issn>1079-2724</issn><issn>1573-8698</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kEtPwzAQhCMEEqXwBzhZ4hxYx8aPY1WeUiUk2p4tO3XSlDQutguEX49LQdw47Ug7s6v5suwcwyUG4FcBgxAkh4LmIFlS5CAb4GtOcsGkOEwauMwLXtDj7CSEFQBIQcQgq0ebjXcfzVpHi8aui961rTZN28QeuQpN7Trpzmr_u0XTPkS7Ru9NXKJp3OVubKt7NA9NV6NZ87J0nXtDz7betto3nzo2rjvNjirdBnv2M4fZ_O52Nn7IJ0_3j-PRJC8LDjHHVQVal1xYVsnCSrNYYG6EBEwLQzgHjotUi3FKtWEGl5RKYxclSCkx14YMs4v93dTqdWtDVCu39V16qQgwJhgVlCZXsXeV3oXgbaU2PiHwvcKgdkDVHqhKQNU3UEVSiOxDIZm72vq_0_-kvgCpo3pS</recordid><startdate>20240601</startdate><enddate>20240601</enddate><creator>Katta, Ravinder</creator><creator>Sukavanam, N.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-1583-4134</orcidid></search><sort><creationdate>20240601</creationdate><title>Approximate Controllability of Semilinear Control System with State Delay Using Tikhonov Regularization</title><author>Katta, Ravinder ; Sukavanam, N.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-1ff0aac78e6f92e9bdd17b890142b37707121576744ab6b1c449bedc099917ab3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Control systems</topic><topic>Controllability</topic><topic>Delay</topic><topic>Dynamical Systems</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Linear systems</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Regularization</topic><topic>Systems Theory</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Katta, Ravinder</creatorcontrib><creatorcontrib>Sukavanam, N.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of dynamical and control systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Katta, Ravinder</au><au>Sukavanam, N.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Approximate Controllability of Semilinear Control System with State Delay Using Tikhonov Regularization</atitle><jtitle>Journal of dynamical and control systems</jtitle><stitle>J Dyn Control Syst</stitle><date>2024-06-01</date><risdate>2024</risdate><volume>30</volume><issue>2</issue><artnum>20</artnum><issn>1079-2724</issn><eissn>1573-8698</eissn><abstract>In this paper computation of control for an approximately controllable semilinear system with state delay is studied using Tikhonov regularization. Depending on the state delay occurred in the time interval, approximate controllability of the semilinear control system is proved under the assumption of approximate controllability of the corresponding linear system without state delay under some assumptions on the system constraints.Computing control for a given target state for the aforesaid system is ill-posed in the sense of Hadamard. Regularized control is computed using Tikhonov regularization for a given target state. Under some assumptions on system and nonlinear function
f
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| source | Springer Nature - Complete Springer Journals |
| subjects | Calculus of Variations and Optimal Control Optimization Control Control systems Controllability Delay Dynamical Systems Dynamical Systems and Ergodic Theory Linear systems Mathematics Mathematics and Statistics Regularization Systems Theory Vibration |
| title | Approximate Controllability of Semilinear Control System with State Delay Using Tikhonov Regularization |
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