An efficient discretization scheme for solving nonlinear optimal control problems with multiple time delays
Summary This paper presents a composite Chebyshev finite difference method to numerically solve nonlinear optimal control problems with multiple time delays. The proposed discretization scheme is based on a hybrid of block‐pulse functions and Chebyshev polynomials using the well‐known Chebyshev Gaus...
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| Veröffentlicht in: | Optimal control applications & methods 2016-07, Vol.37 (4), p.682-707 |
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| container_title | Optimal control applications & methods |
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| creator | Marzban, H. R. Hoseini, S. M. |
| description | Summary
This paper presents a composite Chebyshev finite difference method to numerically solve nonlinear optimal control problems with multiple time delays. The proposed discretization scheme is based on a hybrid of block‐pulse functions and Chebyshev polynomials using the well‐known Chebyshev Gauss–Lobatto points. Our approach is an extension and also a modification of the Chebyshev finite difference scheme. A direct approach is used to transform the delayed optimal control problem into a nonlinear programming problem whose solution is much more easier than the original one. Some useful error bounds are established. In addition, the convergence of the method is discussed. A wide variety of numerical experiments are investigated to show the usefulness and effectiveness of the proposed discretization procedure. The method has a simple structure and can be implemented without too much effort. Copyright © 2015 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/oca.2187 |
| format | Article |
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This paper presents a composite Chebyshev finite difference method to numerically solve nonlinear optimal control problems with multiple time delays. The proposed discretization scheme is based on a hybrid of block‐pulse functions and Chebyshev polynomials using the well‐known Chebyshev Gauss–Lobatto points. Our approach is an extension and also a modification of the Chebyshev finite difference scheme. A direct approach is used to transform the delayed optimal control problem into a nonlinear programming problem whose solution is much more easier than the original one. Some useful error bounds are established. In addition, the convergence of the method is discussed. A wide variety of numerical experiments are investigated to show the usefulness and effectiveness of the proposed discretization procedure. The method has a simple structure and can be implemented without too much effort. Copyright © 2015 John Wiley & Sons, Ltd.</description><identifier>ISSN: 0143-2087</identifier><identifier>EISSN: 1099-1514</identifier><identifier>DOI: 10.1002/oca.2187</identifier><identifier>CODEN: OCAMD5</identifier><language>eng</language><publisher>Glasgow: Blackwell Publishing Ltd</publisher><subject>Chebyshev approximation ; Chebyshev Gauss-Lobatto points ; composite Chebyshev finite difference ; Discretization ; Finite difference method ; hybrid functions ; Mathematical analysis ; Mathematical models ; nonlinear multi-delay ; Nonlinearity ; Optimal control ; Time delay</subject><ispartof>Optimal control applications & methods, 2016-07, Vol.37 (4), p.682-707</ispartof><rights>Copyright © 2015 John Wiley & Sons, Ltd.</rights><rights>Copyright © 2016 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3647-fa08e01f298b66c62de2cc25dfc8b807938bcf70e8656425cc285480ea243f713</citedby><cites>FETCH-LOGICAL-c3647-fa08e01f298b66c62de2cc25dfc8b807938bcf70e8656425cc285480ea243f713</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Foca.2187$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Foca.2187$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27903,27904,45553,45554</link.rule.ids></links><search><creatorcontrib>Marzban, H. R.</creatorcontrib><creatorcontrib>Hoseini, S. M.</creatorcontrib><title>An efficient discretization scheme for solving nonlinear optimal control problems with multiple time delays</title><title>Optimal control applications & methods</title><addtitle>Optim. Control Appl. Meth</addtitle><description>Summary
This paper presents a composite Chebyshev finite difference method to numerically solve nonlinear optimal control problems with multiple time delays. The proposed discretization scheme is based on a hybrid of block‐pulse functions and Chebyshev polynomials using the well‐known Chebyshev Gauss–Lobatto points. Our approach is an extension and also a modification of the Chebyshev finite difference scheme. A direct approach is used to transform the delayed optimal control problem into a nonlinear programming problem whose solution is much more easier than the original one. Some useful error bounds are established. In addition, the convergence of the method is discussed. A wide variety of numerical experiments are investigated to show the usefulness and effectiveness of the proposed discretization procedure. The method has a simple structure and can be implemented without too much effort. Copyright © 2015 John Wiley & Sons, Ltd.</description><subject>Chebyshev approximation</subject><subject>Chebyshev Gauss-Lobatto points</subject><subject>composite Chebyshev finite difference</subject><subject>Discretization</subject><subject>Finite difference method</subject><subject>hybrid functions</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>nonlinear multi-delay</subject><subject>Nonlinearity</subject><subject>Optimal control</subject><subject>Time delay</subject><issn>0143-2087</issn><issn>1099-1514</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp10EFrVDEQB_AgFlxbwY8Q8OLltZO8l7y847LYqhRroeIxZLMTmzYvWZNs6_rpTWlRFDzNYX4M8_8T8prBMQPgJ8maY87U-IwsGExTxwQbnpMFsKHvOKjxBXlZyg0AjKznC3K7jBSd89ZjrHTji81Y_U9TfYq02GuckbqUaUnhzsdvNKYYfESTadpWP5tAbYo1p0C3Oa0DzoXe-3pN512ofhuQNoR0g8HsyxE5cCYUfPU0D8mX03dXq_fd-cXZh9XyvLO9HMbOGVAIzPFJraW0km-QW8vFxlm1VjBOvVpbNwIqKeTARdspMShAw4fetViH5O3j3fbS9x2WqueWC0MwEdOuaKa4EAKkmhp98w-9Sbsc23dNARsnmBT8OWhzKiWj09vcsue9ZqAfWtetdf3QeqPdI733Aff_dfpitfzb-1Lxx29v8q2WYz8K_fXTmYbTCS7lZ6Y_9r8Afc6S_w</recordid><startdate>201607</startdate><enddate>201607</enddate><creator>Marzban, H. R.</creator><creator>Hoseini, S. M.</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope></search><sort><creationdate>201607</creationdate><title>An efficient discretization scheme for solving nonlinear optimal control problems with multiple time delays</title><author>Marzban, H. R. ; Hoseini, S. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3647-fa08e01f298b66c62de2cc25dfc8b807938bcf70e8656425cc285480ea243f713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Chebyshev approximation</topic><topic>Chebyshev Gauss-Lobatto points</topic><topic>composite Chebyshev finite difference</topic><topic>Discretization</topic><topic>Finite difference method</topic><topic>hybrid functions</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>nonlinear multi-delay</topic><topic>Nonlinearity</topic><topic>Optimal control</topic><topic>Time delay</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Marzban, H. R.</creatorcontrib><creatorcontrib>Hoseini, S. M.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Optimal control applications & methods</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Marzban, H. R.</au><au>Hoseini, S. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An efficient discretization scheme for solving nonlinear optimal control problems with multiple time delays</atitle><jtitle>Optimal control applications & methods</jtitle><addtitle>Optim. Control Appl. Meth</addtitle><date>2016-07</date><risdate>2016</risdate><volume>37</volume><issue>4</issue><spage>682</spage><epage>707</epage><pages>682-707</pages><issn>0143-2087</issn><eissn>1099-1514</eissn><coden>OCAMD5</coden><abstract>Summary
This paper presents a composite Chebyshev finite difference method to numerically solve nonlinear optimal control problems with multiple time delays. The proposed discretization scheme is based on a hybrid of block‐pulse functions and Chebyshev polynomials using the well‐known Chebyshev Gauss–Lobatto points. Our approach is an extension and also a modification of the Chebyshev finite difference scheme. A direct approach is used to transform the delayed optimal control problem into a nonlinear programming problem whose solution is much more easier than the original one. Some useful error bounds are established. In addition, the convergence of the method is discussed. A wide variety of numerical experiments are investigated to show the usefulness and effectiveness of the proposed discretization procedure. The method has a simple structure and can be implemented without too much effort. Copyright © 2015 John Wiley & Sons, Ltd.</abstract><cop>Glasgow</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/oca.2187</doi><tpages>26</tpages></addata></record> |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Chebyshev approximation Chebyshev Gauss-Lobatto points composite Chebyshev finite difference Discretization Finite difference method hybrid functions Mathematical analysis Mathematical models nonlinear multi-delay Nonlinearity Optimal control Time delay |
| title | An efficient discretization scheme for solving nonlinear optimal control problems with multiple time delays |
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