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Idioma: Inglés
Editorial: Cambridge University Press, 2010
Serie: Encyclopedia of Mathematics and its Applications, Libro 66 de 188. Libro 66 de 188 - Encyclopedia of Mathematics and its Applications
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Librería: LIBRERIA LEA+, Santiago, RM, ChileLIBRERIA LEA+
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Blanda. Condición: New. Estado de la sobrecubierta: Nuevo. 0. Paperback Re-issue. Originally published in 2000 , this is the first volume two - volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon and related differential ( integral ) and algebraic Riccati… equations . Both continuous theory and numerical approximation theory are included . An abstract space treatment is provided , which is based on semi group methods , and which is unifying across a few basic classes of evolution . A key feature of this treatise is the wealth of concrete multidimen sional POE illustrations , which fit naturally into the abstract theory , with no artificial assumptions imposed , at both the continuous and numerical level . Throughout these volumes , emphasis is placed on unbounded control operators or on unbounded observation operators as they arise in the context of various abstract frameworks that are motivated by partial differential equations with boundary / point control . Relevant classes of POEs include : parabolic or parabolic - like equations , hyperbolic and Petrowski - type equations ( such as plate equations and the Schrödinger equation ) , and hybrid systems of coupled POES of the type that arise in modern thermo - elastic and smart material applications . Purely POE dynamical properties are critical in motivating the various abstract settings and in applying the corresponding theories to concrete POEs arising in mathematical physics and in other recent technological applications . Volume I covers the abstract parabolic theory , including both the finite and infinite horizon optimal control problems , as well as the corresponding min - max theory with nondefinite quadratic cost . A lengthy chapter presents many multidimensional POE illustrations with boundary / point control and observation . These include not only the traditional parabolic equations , such as the heat equation , but also second - order equations with structural ( " high " ) damping , as well as thermo - elastic plate dynamical properties are provided in detail . Volume II is focused on the optimal control problem over a finite time interval for hyperbolic dynamical systems including second - order hyperbolic equations with Dirichlet boundaries , plate equations and the Schrödinger equation under a variety of boundary controls , and structural acoustic models coupling two hyperbolic equations. 920 gr. No Aplica (ilustrador). Libro.
