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001 978-0-8176-8149-4
003 DE-He213
005 20140220083711.0
007 cr nn 008mamaa
008 110805s2011 xxu| s |||| 0|eng d
020 _a9780817681494
_9978-0-8176-8149-4
024 7 _a10.1007/978-0-8176-8149-4
_2doi
050 4 _aQ295
050 4 _aQA402.3-402.37
072 7 _aGPFC
_2bicssc
072 7 _aSCI064000
_2bisacsh
072 7 _aTEC004000
_2bisacsh
082 0 4 _a519
_223
100 1 _aKogut, Peter I.
_eauthor.
245 1 0 _aOptimal Control Problems for Partial Differential Equations on Reticulated Domains
_h[electronic resource] :
_bApproximation and Asymptotic Analysis /
_cby Peter I. Kogut, Günter R. Leugering.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2011.
300 _aXVI, 636p. 26 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSystems & Control: Foundations & Applications
505 0 _aIntroduction -- Part I. Asymptotic Analysis of Optimal Control Problems for Partial Differential Equations: Basic Tools -- Background Material on Asymptotic Analysis of External Problems -- Variational Methods of Optimal Control Theory -- Suboptimal and Approximate Solutions to External Problems -- Introduction to the Asymptotic Analysis of Optimal Control Problems: A Parade of Examples -- Convergence Concepts in Variable Banach Spaces -- Convergence of Sets in Variable Spaces -- Passing to the Limit in Constrained Minimization Problems -- Part II. Optimal Control Problems on Periodic Reticulated Domains: Asymptotic Analysis and Approximate Solutions -- Suboptimal Control of Linear Steady-States Processes on Thin Periodic Structures with Mixed Boundary Controls -- Approximate Solutions of Optimal Control Problems for Ill-Posed Objects on Thin Periodic Structures -- Asymptotic Analysis of Optimal Control Problems on Periodic Singular Structures -- Suboptimal Boundary Control of Elliptic Equations in Domains with Small Holes -- Asymptotic Analysis of Elliptic Optimal Control Problems in Thick Multi-Structures with Dirichlet and Neumann Boundary Controls -- Gap Phenomenon in Modeling of Suboptimal Controls to Parabolic Optimal Control Problems in Thick Multi-Structures -- Boundary Velocity Suboptimal Control of Incompressible Flow in Cylindrically Perforated Domains -- Optimal Control Problems in Coefficients: Sensitivity Analysis and Approximation -- References -- Index.
520 _aAfter over 50 years of increasing scientific interest, optimal control of partial differential equations (PDEs) has developed into a well-established discipline in mathematics with myriad applications to science and engineering. As the field has grown, so too has the complexity of the systems it describes; the numerical realization of optimal controls has become increasingly difficult, demanding ever more sophisticated mathematical tools.  A comprehensive monograph on the subject, Optimal Control of Partial Differential Equations on Reticulated Domains is intended to address some of the obstacles that face researchers today, particularly with regard to multi-scale engineering applications involving hierarchies of grid-like domains. Bringing original results together with others previously scattered across the literature, it tackles computational challenges by exploiting asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs. The book consists of two parts, the first of which can be viewed as a compendium of modern optimal control theory in Banach spaces. The second part is a focused, in-depth, and self-contained study of the asymptotics of optimal control problems related to reticulated domains—the first such study in the literature. Specific topics covered in the work include: * a mostly self-contained mathematical theory of PDEs on reticulated domains; * the concept of optimal control problems for PDEs in varying such domains, and hence, in varying Banach spaces; * convergence of optimal control problems in variable spaces; * an introduction to the asymptotic analysis of optimal control problems; * optimal control problems dealing with ill-posed objects on thin periodic structures, thick periodic singular graphs, thick multi-structures with Dirichlet and Neumann boundary controls, and coefficients on reticulated structures. Serving as both a text on abstract optimal control problems and a monograph where specific applications are explored, this book is an excellent reference for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aSystems theory.
650 0 _aMathematical optimization.
650 0 _aEngineering mathematics.
650 0 _aMechanical engineering.
650 1 4 _aMathematics.
650 2 4 _aSystems Theory, Control.
650 2 4 _aControl.
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
650 2 4 _aPartial Differential Equations.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aStructural Mechanics.
700 1 _aLeugering, Günter R.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817681487
830 0 _aSystems & Control: Foundations & Applications
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-8149-4
912 _aZDB-2-SMA
999 _c105098
_d105098