Versions of inexact Kleinman‐Newton methods for Riccati equations
Identifieur interne : 000737 ( Istex/Corpus ); précédent : 000736; suivant : 000738Versions of inexact Kleinman‐Newton methods for Riccati equations
Auteurs : Timo Hylla ; E. W. SachsSource :
- PAMM [ 1617-7061 ] ; 2007-12.
Abstract
Optimal control problems involving PDEs often lead in practice to the numerical computation of feedback laws for an optimal control. This is achieved through the solution of a Riccati equation which can be large scale, since the discretized problems are large scale and require special attention in their numerical solution. The Kleinman‐Newton method is a classical way to solve an algebraic Riccati equation. We look at two versions of an extension of this method to an inexact Newton method. It can be shown that these two implementable versions of Newton's method are identical in the exact case, but differ substantially for the inexact Newton method. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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DOI: 10.1002/pamm.200700766
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This is achieved through the solution of a Riccati equation which can be large scale, since the discretized problems are large scale and require special attention in their numerical solution. The Kleinman‐Newton method is a classical way to solve an algebraic Riccati equation. We look at two versions of an extension of this method to an inexact Newton method. It can be shown that these two implementable versions of Newton's method are identical in the exact case, but differ substantially for the inexact Newton method. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>Timo Hylla</name><affiliations><json:string>University of Trier, Department of Mathematics, 54286 Trier, Germany</json:string><json:string>Phone: +00 49 651 2013470, Fax: +00 49 651 2013473</json:string></affiliations></json:item><json:item><name>E. W. 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Ito</name></json:item></author><host><volume>29</volume><pages><last>515</last><first>499</first></pages><author></author><title>SIAM Journal on Control and Optimization</title></host><title>A Numerical Algorithm for Optimal Feedback Gains in High Dimensional Linear Quadratic Regulator Problems</title></json:item><json:item><host><author></author><title>Inexact Kleinman‐Newton Method for Riccati equations, University of Trier, preprint (2007).</title></host></json:item><json:item><host><author></author><title>Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia (1995).</title></host></json:item><json:item><author><json:item><name>D. Kleinman</name></json:item></author><host><volume>13</volume><pages><last>115</last><first>114</first></pages><author></author><title>IEEE Transactions on Automatic Control</title></host><title>On an Iterative Technique for Riccati Equation Computations</title></json:item><json:item><host><author></author><title>Solution of Algebraic Riccati Equations Arising in Control of Partial Differential Equations, in Control and Boundary Analysis, J.P. Zolesio and J. Cagnol, eds., Lecture Notes in Pure Appl. 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The Kleinman‐Newton method is a classical way to solve an algebraic Riccati equation. We look at two versions of an extension of this method to an inexact Newton method. It can be shown that these two implementable versions of Newton's method are identical in the exact case, but differ substantially for the inexact Newton method. (© 2008 WILEY‐VCH Verlag GmbH & Co. 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