Inverse optimality of adaptive control for Korteweg-de Vries-Burgers equation
The Korteweg-de Vries-Burgers (KdVB) equation is one of the simplest nonlinear mathematical models, which is used to model motion of waves in a variety of fluid flow processes. And inverse optimality allows the design of optimal control laws, which may minimize/maximize a physical quantity of intere...
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| Veröffentlicht in: | International journal of dynamics and control 2024-02, Vol.12 (2), p.486-493 |
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| creator | Cai, Xiushan Lin, Yuhang Lin, Cong Liu, Leipo |
| description | The Korteweg-de Vries-Burgers (KdVB) equation is one of the simplest nonlinear mathematical models, which is used to model motion of waves in a variety of fluid flow processes. And inverse optimality allows the design of optimal control laws, which may minimize/maximize a physical quantity of interest and which may possess certain robustness margins, without the need to solve a Hamilton-Jacobi-Isaacs partial differential equation (PDE) that may not be possible to solve. Therefore, it is important to study inverse optimal control for KdVB equation. In this paper, it is proved that the boundary control of Balogh and Krstic (IEEE Trans Autom Control 45(9):1739-1745, 2000) is inverse optimal for a meaningful functional. Next, an adaptive boundary control design for KdVB equation with an unknown dissipation coefficient is presented. Furthermore, it is shown that this adaptive control design is also inverse optimal for a meaningful functional. Two examples are given to illustrate the validity of the proposed design. |
| doi_str_mv | 10.1007/s40435-023-01195-5 |
| format | Article |
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Two examples are given to illustrate the validity of the proposed design.</description><subject>Adaptive control</subject><subject>Boundary control</subject><subject>Burgers equation</subject><subject>Complexity</subject><subject>Control</subject><subject>Control and Systems Theory</subject><subject>Control theory</subject><subject>Dynamical Systems</subject><subject>Engineering</subject><subject>Fluid flow</subject><subject>Mathematical models</subject><subject>Optimal control</subject><subject>Optimization</subject><subject>Partial differential equations</subject><subject>Robustness (mathematics)</subject><subject>Vibration</subject><issn>2195-268X</issn><issn>2195-2698</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kM1OwzAQhC0EElXpC3CyxNmwduw4OULFT0URF0DcLMd2qlQlTu2kqG-PSxDcOO2sNDOr_RA6p3BJAeRV5MAzQYBlBCgtBRFHaMIOguVlcfyri_dTNItxDQCMcmC8nKCnRbtzITrsu7750Jum32NfY2112ncOG9_2wW9w7QN-9KF3n25FrMNvoXGR3AxhldLYbQfdN749Qye13kQ3-5lT9Hp3-zJ_IMvn-8X8ekkMk9CTMrPSMGNKarNKcy5lZZwuuMyodQI0l7zSkBd5XQkhmeXW1KzKpRQiN2BdNkUXY28X_HZwsVdrP4Q2nVSsZHkOTCQkU8RGlwk-xuBq1YX0Y9grCupATo3kVCKnvskpkULZGIrJ3Kbv_qr_SX0BWLhxTA</recordid><startdate>20240201</startdate><enddate>20240201</enddate><creator>Cai, Xiushan</creator><creator>Lin, Yuhang</creator><creator>Lin, Cong</creator><creator>Liu, Leipo</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9698-9148</orcidid></search><sort><creationdate>20240201</creationdate><title>Inverse optimality of adaptive control for Korteweg-de Vries-Burgers equation</title><author>Cai, Xiushan ; Lin, Yuhang ; Lin, Cong ; Liu, Leipo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-93d7c2cc91d3ba4477bcea84731de50a474ba0686fb5572d4dcf2b677556c0de3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Adaptive control</topic><topic>Boundary control</topic><topic>Burgers equation</topic><topic>Complexity</topic><topic>Control</topic><topic>Control and Systems Theory</topic><topic>Control theory</topic><topic>Dynamical Systems</topic><topic>Engineering</topic><topic>Fluid flow</topic><topic>Mathematical models</topic><topic>Optimal control</topic><topic>Optimization</topic><topic>Partial differential equations</topic><topic>Robustness (mathematics)</topic><topic>Vibration</topic><toplevel>online_resources</toplevel><creatorcontrib>Cai, Xiushan</creatorcontrib><creatorcontrib>Lin, Yuhang</creatorcontrib><creatorcontrib>Lin, Cong</creatorcontrib><creatorcontrib>Liu, Leipo</creatorcontrib><collection>CrossRef</collection><jtitle>International journal of dynamics and control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cai, Xiushan</au><au>Lin, Yuhang</au><au>Lin, Cong</au><au>Liu, Leipo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Inverse optimality of adaptive control for Korteweg-de Vries-Burgers equation</atitle><jtitle>International journal of dynamics and control</jtitle><stitle>Int. 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| subjects | Adaptive control Boundary control Burgers equation Complexity Control Control and Systems Theory Control theory Dynamical Systems Engineering Fluid flow Mathematical models Optimal control Optimization Partial differential equations Robustness (mathematics) Vibration |
| title | Inverse optimality of adaptive control for Korteweg-de Vries-Burgers equation |
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