Ivan V. Sergienko, Vasyl S. Deineka

Optimal Control of Distributed Systems with Conjugation Conditions (eBook, PDF)

Redaktion: Shor, Naum Z.

• Format: PDF

Produktbeschreibung

This work develops the methodology according to which classes of discontinuous functions are used in order to investigate a correctness of boundary-value and initial boundary-value problems for the cases with elliptic, parabolic, pseudoparabolic, hyperbolic, and pseudohyperbolic equations and with elasticity theory equation systems that have nonsmooth solutions, including discontinuous solutions.

With the basis of this methodology, the monograph shows a continuous dependence of states, namely, of solutions to the enumerated boundary-value and initial boundary-value problems (including discontinuous states) and a dependence of solution traces on distributed controls and controls at sectors of n-dimensional domain boundaries and at n-1-dimensional function-state discontinuity surfaces (i.e., at mean surfaces of thin inclusions in heterogeneous media). Such an aspect provides the existence of optimal controls for the mentioned systems with J.L. Lions' quadratic cost functionals.

Besides this, the authors consider some new systems, for instance, the ones described by the conditionally correct Neumann problems with unique states on convex sets, and such states admit first-order discontinuities. These systems are also described by quartic equations with conjugation conditions, by parabolic equations with constraints that contain first-order time state derivatives in the presence of concentrated heat capacity, and by elasticity theory equations.

In a number of cases, when a set of feasible controls coincides with corresponding Hilbert spaces, the authors propose to use the computational algorithms for the finite-element method. Such algorithms have the increased order of the accuracy with which optimal controls are numerically found.

Audience

This book is intended for specialists in applied mathematics, scientific researchers, engineers, and postgraduate students interested in optimal control ofheterogeneous distributed systems with states described by boundary-value and initial boundary-value problems.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 383
• Erscheinungstermin: 19. September 2005
• Englisch
• ISBN-13: 9780387242569
• Artikelnr.: 37288355

Autorenporträt

Ivan V. Sergienko, V.M. Glushkov Institute of Cybernetics, Kiev, Ukraine / Vasyl S. Deineka, V.M. Glushkov Institute of Cybernetics, Kiev, Ukraine

Inhaltsangabe

Control of Systems Described by Elliptic-Type Partial-Differential Equations under Conjugation Conditions.- Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation under Conjugation Conditions.- Control of a System Described by a One-Dimensional Quartic Equation under Conjugation Conditions.- Control of a System Described by a Two-Dimensional Quartic Equation under Conjugation Conditions.- Control of a System Described by a Parabolic Equation under Conjugation Conditions.- Control of a System Described by a Parabolic Equation in the Presence of Concentrated Heat Capacity.- Control of a System Described by a Pseudoparabolic Equation under Conjugation Conditions.- Control of a System Described by a Hyperbolic Equation under Conjugation Conditions.- Control of a System Described by a Pseudohyperbolic Equation under Conjugation Conditions.- Optimal Control of a Deformed Complicated Solid Body State.

Rezensionen

From the reviews of the first edition: "The book is devoted to a special class of linear-quadratic optimal control problems governed by partial differential equations ... . the book gives a clear enough understanding of properties of optimal control problems for the basic cases of nonstandard conjugation conditions (including controls) on the interface between the two domains." (Uldis Raitums, Zentralblatt MATH, Vol. 1080, 2006)