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Adjustment Optimization for a Model of Differential Realization of a Multidimensional Second-Order System
We study the problem of calculating the preferred differential realization system in the space of similar plant-controller-observer models induced by transformation groups over an identified second-order dynamical system. We prove theorems on the existence of a transforming matrix (an a posteriori b...
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| Published in: | Differential equations 2019-10, Vol.55 (10), p.1390-1396 |
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| container_title | Differential equations |
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| creator | Rusanov, V. A. Daneev, A. V. Linke, Yu. E. |
| description | We study the problem of calculating the preferred differential realization system in the space of similar plant-controller-observer models induced by transformation groups over an identified second-order dynamical system. We prove theorems on the existence of a transforming matrix (an a posteriori basis of the configuration space) in the transformation groups
GL
n
(ℝ) and
SO
n
minimizing the mismatch between the positional force matrix and its reference rated parameters. Based on Morse theory, we construct a nonlinear matrix characteristic equation of the optimal
SO
n
-adjustment process. The results have applications in the differential precise modeling of forced oscillations and generate statements of the problem in the infinite-dimensional case. |
| doi_str_mv | 10.1134/S0012266119100148 |
| format | article |
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GL
n
(ℝ) and
SO
n
minimizing the mismatch between the positional force matrix and its reference rated parameters. Based on Morse theory, we construct a nonlinear matrix characteristic equation of the optimal
SO
n
-adjustment process. The results have applications in the differential precise modeling of forced oscillations and generate statements of the problem in the infinite-dimensional case.</description><identifier>ISSN: 0012-2661</identifier><identifier>EISSN: 1608-3083</identifier><identifier>DOI: 10.1134/S0012266119100148</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Control Theory ; Difference and Functional Equations ; Differential equations ; Eigenvalues ; Eigenvectors ; Existence theorems ; Mathematics ; Mathematics and Statistics ; Optimization ; Ordinary Differential Equations ; Partial Differential Equations ; Transformations (mathematics)</subject><ispartof>Differential equations, 2019-10, Vol.55 (10), p.1390-1396</ispartof><rights>Pleiades Publishing, Ltd. 2019</rights><rights>COPYRIGHT 2019 Springer</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-553b2da47691582237c2e5f1c8c608d4837df97636e77d0dd15832791f9c98293</citedby><cites>FETCH-LOGICAL-c355t-553b2da47691582237c2e5f1c8c608d4837df97636e77d0dd15832791f9c98293</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Rusanov, V. A.</creatorcontrib><creatorcontrib>Daneev, A. V.</creatorcontrib><creatorcontrib>Linke, Yu. E.</creatorcontrib><title>Adjustment Optimization for a Model of Differential Realization of a Multidimensional Second-Order System</title><title>Differential equations</title><addtitle>Diff Equat</addtitle><description>We study the problem of calculating the preferred differential realization system in the space of similar plant-controller-observer models induced by transformation groups over an identified second-order dynamical system. We prove theorems on the existence of a transforming matrix (an a posteriori basis of the configuration space) in the transformation groups
GL
n
(ℝ) and
SO
n
minimizing the mismatch between the positional force matrix and its reference rated parameters. Based on Morse theory, we construct a nonlinear matrix characteristic equation of the optimal
SO
n
-adjustment process. The results have applications in the differential precise modeling of forced oscillations and generate statements of the problem in the infinite-dimensional case.</description><subject>Control Theory</subject><subject>Difference and Functional Equations</subject><subject>Differential equations</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Existence theorems</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Optimization</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>Transformations (mathematics)</subject><issn>0012-2661</issn><issn>1608-3083</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kUtLAzEUhYMoWKs_wN2A69E8ZibJstQnVApW10PMo6TMTGqSLuqv95ZRXIjcRS73fOdywkXokuBrQlh1s8KYUNo0hEgCbSWO0IQ0WJQMC3aMJge5POin6CylDcZYclJPkJ-ZzS7l3g65WG6z7_2nyj4MhQuxUMVzMLYrgituvXM2AuVVV7xY1f1woAG267I3HrYkmAGxsjoMplxGY2Ox2qds-3N04lSX7MX3O0Vv93ev88dysXx4ms8WpWZ1ncu6Zu_UqIo3ktSCUsY1tbUjWmj4jqkE48ZJ3rDGcm6wMUAxyiVxUktBJZuiq3HvNoaPnU253YRdhFCppYxUVGAiGqCuR2qtOtv6wYUclYYytveQ3ToP8xmnWEhaCQoGMhp0DClF69pt9L2K-5bg9nCC9s8JwENHTwJ2WNv4G-V_0xeBRIbc</recordid><startdate>20191001</startdate><enddate>20191001</enddate><creator>Rusanov, V. A.</creator><creator>Daneev, A. V.</creator><creator>Linke, Yu. E.</creator><general>Pleiades Publishing</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20191001</creationdate><title>Adjustment Optimization for a Model of Differential Realization of a Multidimensional Second-Order System</title><author>Rusanov, V. A. ; Daneev, A. V. ; Linke, Yu. E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-553b2da47691582237c2e5f1c8c608d4837df97636e77d0dd15832791f9c98293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Control Theory</topic><topic>Difference and Functional Equations</topic><topic>Differential equations</topic><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Existence theorems</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Optimization</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><topic>Transformations (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rusanov, V. A.</creatorcontrib><creatorcontrib>Daneev, A. V.</creatorcontrib><creatorcontrib>Linke, Yu. E.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rusanov, V. A.</au><au>Daneev, A. V.</au><au>Linke, Yu. E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adjustment Optimization for a Model of Differential Realization of a Multidimensional Second-Order System</atitle><jtitle>Differential equations</jtitle><stitle>Diff Equat</stitle><date>2019-10-01</date><risdate>2019</risdate><volume>55</volume><issue>10</issue><spage>1390</spage><epage>1396</epage><pages>1390-1396</pages><issn>0012-2661</issn><eissn>1608-3083</eissn><abstract>We study the problem of calculating the preferred differential realization system in the space of similar plant-controller-observer models induced by transformation groups over an identified second-order dynamical system. We prove theorems on the existence of a transforming matrix (an a posteriori basis of the configuration space) in the transformation groups
GL
n
(ℝ) and
SO
n
minimizing the mismatch between the positional force matrix and its reference rated parameters. Based on Morse theory, we construct a nonlinear matrix characteristic equation of the optimal
SO
n
-adjustment process. The results have applications in the differential precise modeling of forced oscillations and generate statements of the problem in the infinite-dimensional case.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0012266119100148</doi><tpages>7</tpages></addata></record> |
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| ispartof | Differential equations, 2019-10, Vol.55 (10), p.1390-1396 |
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| language | eng |
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| subjects | Control Theory Difference and Functional Equations Differential equations Eigenvalues Eigenvectors Existence theorems Mathematics Mathematics and Statistics Optimization Ordinary Differential Equations Partial Differential Equations Transformations (mathematics) |
| title | Adjustment Optimization for a Model of Differential Realization of a Multidimensional Second-Order System |
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