Optimal Control of Self-Adjoint Systems
Given the system ẋ(t)=A(t)x(t)+u(t),where A(t)=-A'(t) and ||u(t)||≤1, it will be shown that the control u=-x(t)/||x(t)|| drives any initial state to zero in such a manner that the response time, the consumed fuel, and a linear combination of time and control energy are minnimized. The theory is...
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| Veröffentlicht in: | IEEE transactions on applications and industry 1964-05, Vol.83 (72), p.161-166 |
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| container_end_page | 166 |
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| container_issue | 72 |
| container_start_page | 161 |
| container_title | IEEE transactions on applications and industry |
| container_volume | 83 |
| creator | Athans, Michael Falb, P. L. Lacoss, R. T. |
| description | Given the system ẋ(t)=A(t)x(t)+u(t),where A(t)=-A'(t) and ||u(t)||≤1, it will be shown that the control u=-x(t)/||x(t)|| drives any initial state to zero in such a manner that the response time, the consumed fuel, and a linear combination of time and control energy are minnimized. The theory is applied to the optimum angular velocity cotrol of a tumbling space body. |
| doi_str_mv | 10.1109/TAI.1964.5407784 |
| format | Article |
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The theory is applied to the optimum angular velocity cotrol of a tumbling space body.</description><identifier>ISSN: 0536-1524</identifier><identifier>EISSN: 2379-6782</identifier><identifier>DOI: 10.1109/TAI.1964.5407784</identifier><language>eng</language><publisher>IEEE</publisher><subject>Automatic control ; Costs ; Equations ; Feeds ; Laboratories ; Machining ; Metalworking machines ; Milling ; Optimal control ; Surface finishing</subject><ispartof>IEEE transactions on applications and industry, 1964-05, Vol.83 (72), p.161-166</ispartof><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c263t-cb3f981219ef766455108a862786515fcd15f28dcf514a5d86b54ed6e4a332e93</citedby><cites>FETCH-LOGICAL-c263t-cb3f981219ef766455108a862786515fcd15f28dcf514a5d86b54ed6e4a332e93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/5407784$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/5407784$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Athans, Michael</creatorcontrib><creatorcontrib>Falb, P. L.</creatorcontrib><creatorcontrib>Lacoss, R. T.</creatorcontrib><title>Optimal Control of Self-Adjoint Systems</title><title>IEEE transactions on applications and industry</title><addtitle>TAI</addtitle><description>Given the system ẋ(t)=A(t)x(t)+u(t),where A(t)=-A'(t) and ||u(t)||≤1, it will be shown that the control u=-x(t)/||x(t)|| drives any initial state to zero in such a manner that the response time, the consumed fuel, and a linear combination of time and control energy are minnimized. The theory is applied to the optimum angular velocity cotrol of a tumbling space body.</description><subject>Automatic control</subject><subject>Costs</subject><subject>Equations</subject><subject>Feeds</subject><subject>Laboratories</subject><subject>Machining</subject><subject>Metalworking machines</subject><subject>Milling</subject><subject>Optimal control</subject><subject>Surface finishing</subject><issn>0536-1524</issn><issn>2379-6782</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1964</creationdate><recordtype>article</recordtype><recordid>eNo9jzFrwzAQRkVpoW7avdDFWye5Okl3ksZg2jQQyJB0Fo4tgYMTB8tL_n0dknb5bvjuHfcYewVRAAj3sZ0vC3CkC9TCGKvvWCaVcZyMlfcsE6iIA0r9yJ5S2guBBEJn7H19GttD1eVlfxyHvsv7mG9CF_m82fftccw35zSGQ3pmD7HqUni5zRn7-frclt98tV4sy_mK15LUyOudis6CBBeiIdKIIGxlSRpLCBjrZgppmzoi6AobSzvUoaGgK6VkcGrGxPVuPfQpDSH60zD9N5w9CH8R9ZOov4j6m-iEvF2RNoTwv_7X_gJxyk1B</recordid><startdate>196405</startdate><enddate>196405</enddate><creator>Athans, Michael</creator><creator>Falb, P. L.</creator><creator>Lacoss, R. T.</creator><general>IEEE</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>196405</creationdate><title>Optimal Control of Self-Adjoint Systems</title><author>Athans, Michael ; Falb, P. L. ; Lacoss, R. T.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c263t-cb3f981219ef766455108a862786515fcd15f28dcf514a5d86b54ed6e4a332e93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1964</creationdate><topic>Automatic control</topic><topic>Costs</topic><topic>Equations</topic><topic>Feeds</topic><topic>Laboratories</topic><topic>Machining</topic><topic>Metalworking machines</topic><topic>Milling</topic><topic>Optimal control</topic><topic>Surface finishing</topic><toplevel>online_resources</toplevel><creatorcontrib>Athans, Michael</creatorcontrib><creatorcontrib>Falb, P. L.</creatorcontrib><creatorcontrib>Lacoss, R. T.</creatorcontrib><collection>CrossRef</collection><jtitle>IEEE transactions on applications and industry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Athans, Michael</au><au>Falb, P. L.</au><au>Lacoss, R. T.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal Control of Self-Adjoint Systems</atitle><jtitle>IEEE transactions on applications and industry</jtitle><stitle>TAI</stitle><date>1964-05</date><risdate>1964</risdate><volume>83</volume><issue>72</issue><spage>161</spage><epage>166</epage><pages>161-166</pages><issn>0536-1524</issn><eissn>2379-6782</eissn><abstract>Given the system ẋ(t)=A(t)x(t)+u(t),where A(t)=-A'(t) and ||u(t)||≤1, it will be shown that the control u=-x(t)/||x(t)|| drives any initial state to zero in such a manner that the response time, the consumed fuel, and a linear combination of time and control energy are minnimized. The theory is applied to the optimum angular velocity cotrol of a tumbling space body.</abstract><pub>IEEE</pub><doi>10.1109/TAI.1964.5407784</doi><tpages>6</tpages></addata></record> |
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| identifier | ISSN: 0536-1524 |
| ispartof | IEEE transactions on applications and industry, 1964-05, Vol.83 (72), p.161-166 |
| issn | 0536-1524 2379-6782 |
| language | eng |
| recordid | cdi_ieee_primary_5407784 |
| source | IEEE Electronic Library (IEL) |
| subjects | Automatic control Costs Equations Feeds Laboratories Machining Metalworking machines Milling Optimal control Surface finishing |
| title | Optimal Control of Self-Adjoint Systems |
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