Optimal Control Of Systems Governed By Partial Differential Equation

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Optimal Control of Systems Governed by Partial Differential Equations

Author : Jacques Louis Lions
Publisher : Springer
ISBN 13 : 9783642650260
Total Pages : 400 pages
Book Rating : 4.6/5 (52 download)

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Book Synopsis Optimal Control of Systems Governed by Partial Differential Equations by : Jacques Louis Lions

Download or read book Optimal Control of Systems Governed by Partial Differential Equations written by Jacques Louis Lions and published by Springer. This book was released on 2011-11-12 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. The development of a theory of optimal control (deterministic) requires the following initial data: (i) a control u belonging to some set ilIi ad (the set of 'admissible controls') which is at our disposition, (ii) for a given control u, the state y(u) of the system which is to be controlled is given by the solution of an equation (*) Ay(u)=given function ofu where A is an operator (assumed known) which specifies the system to be controlled (A is the 'model' of the system), (iii) the observation z(u) which is a function of y(u) (assumed to be known exactly; we consider only deterministic problems in this book), (iv) the "cost function" J(u) ("economic function") which is defined in terms of a numerical function z-+

Optimal Control of Partial Differential Equations

Author : Karl-Heinz Hoffmann
Publisher : Springer Science & Business Media
ISBN 13 : 9783764361518
Total Pages : 344 pages
Book Rating : 4.3/5 (615 download)

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Book Synopsis Optimal Control of Partial Differential Equations by : Karl-Heinz Hoffmann

Download or read book Optimal Control of Partial Differential Equations written by Karl-Heinz Hoffmann and published by Springer Science & Business Media. This book was released on 1999 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-posedness of Semilinear Heat Equations with Iterated Logarithms.- Uniform Stability of Nonlinear Thermoelastic Plates with Free Boundary Conditions.- Exponential Bases in Sobolev Spaces in Control and Observation Problems.- Sampling and Interpolation of Functions with Multi-Band Spectra and Controllability Problems.- Discretization of the Controllability Grammian in View of Exact Boundary Control: the Case of Thin Plates.- Stability of Holomorphic Semigroup Systems under Nonlinear Boundary Perturbations.- Shape Control in Hyperbolic Problems.- Second Order Optimality Conditions for Some Control Problems of Semilinear Elliptic Equations with Integral State Constraints.- Intrinsic P(2, 1) Thin Shell Models and Naghdi's Models without A Priori Assumption on the Stress Tensor.- On the Approximate Controllability for some Explosive Parabolic Problems.- Fréchet-Differentiability and Sufficient Optimality Conditions for Shape Functionals.- State Constrained Optimal Control for some Quasilinear Parabolic Equations.- Controllability property for the Navier-Stokes equations.- Shape Sensitivity and Large Deformation of the Domain for Norton-Hoff Flows.- On a Distributed Control Law with an Application to the Control of Unsteady Flow around a Cylinder.- Homogenization of a Model Describing Vibration of Nonlinear Thin Plates Excited by Piezopatches.- Stabilization of the Dynamic System of Elasticity by Nonlinear Boundary Feedback.- Griffith Formula and Rice-Cherepanov's Integral for Elliptic Equations with Unilateral Conditions in Nonsmooth Domains.- A Domain Optimization Problem for a Nonlinear Thermoelastic System.- Approximate Controllability for a Hydro-Elastic Model in a Rectangular Domain.- Noncooperative Games with Elliptic Systems.- Incomplete Indefinite Decompositions as Multigrid Smoothers for KKT Systems.- Domain Optimization for the Navier-Stokes Equations by an Embedding Domain Method.- On the Approximation and Optimization of Fourth Order Elliptic Systems.- On the Existence and Approximation of Solutions for the Optimal Control of Nonlinear Hyperbolic Conservation Laws.- Identification of Memory Kernels in Heat Conduction and Viscoelasticity.- Variational Formulation for Incompressible Euler Equation by Weak Shape Evolution.

Large-Scale PDE-Constrained Optimization

Author : Lorenz T. Biegler
Publisher : Springer Science & Business Media
ISBN 13 : 364255508X
Total Pages : 347 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Large-Scale PDE-Constrained Optimization by : Lorenz T. Biegler

Download or read book Large-Scale PDE-Constrained Optimization written by Lorenz T. Biegler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.

Real-time PDE-constrained Optimization

Author : Lorenz T. Biegler
Publisher : SIAM
ISBN 13 : 9780898718935
Total Pages : 335 pages
Book Rating : 4.7/5 (189 download)

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Book Synopsis Real-time PDE-constrained Optimization by : Lorenz T. Biegler

Download or read book Real-time PDE-constrained Optimization written by Lorenz T. Biegler and published by SIAM. This book was released on 2007-01-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.

Optimal Control of Partial Differential Equations

Author : Fredi Tröltzsch
Publisher : American Mathematical Society
ISBN 13 : 1470476444
Total Pages : 417 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Optimal Control of Partial Differential Equations by : Fredi Tröltzsch

Download or read book Optimal Control of Partial Differential Equations written by Fredi Tröltzsch and published by American Mathematical Society. This book was released on 2024-03-21 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

Optimal Control of Partial Differential Equations

Author : Andrea Manzoni
Publisher : Springer Nature
ISBN 13 : 3030772268
Total Pages : 507 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Optimal Control of Partial Differential Equations by : Andrea Manzoni

Download or read book Optimal Control of Partial Differential Equations written by Andrea Manzoni and published by Springer Nature. This book was released on 2022-01-01 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.

Optimal Control of Distributed Systems with Conjugation Conditions

Author : Ivan V. Sergienko
Publisher : Springer Science & Business Media
ISBN 13 : 9781402081088
Total Pages : 410 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Optimal Control of Distributed Systems with Conjugation Conditions by : Ivan V. Sergienko

Download or read book Optimal Control of Distributed Systems with Conjugation Conditions written by Ivan V. Sergienko and published by Springer Science & Business Media. This book was released on 2005-02-10 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: At present, in order to resolve problems of ecology and to save mineral resources for future population generations, it is quite necessary to know how to maintain nature arrangement in an efficient way. It is possible to achieve a rational nature arrangement when analyzing solutions to problems concerned with optimal control of distributed systems and with optimization of modes in which main ground medium processes are functioning (motion of liquids, generation of temperature fields, mechanical deformation of multicomponent media). Such analysis becomes even more difficult because of heterogeneity of the region that is closest to the Earth surface, and thin inclusions/cracks in it exert their essential influence onto a state and development of the mentioned processes, especially in the cases of mining. Many researchers, for instance, A.N. Tikhonov - A.A. Samarsky [121], L. Luckner - W.M. Shestakow [65], Tien-Mo Shih, K.L. Johnson [47], E. Sanchez-Palencia [94] and others stress that it is necessary to consider how thin inclusions/cracks exert their influences onto development of these processes, while such inclusions differ in characteristics from main media to a considerable extent (moisture permeability, permeability to heat, bulk density or shear strength may be mentioned). Xll An influence exerted from thin interlayers onto examined processes is taken into account sufficiently adequately by means of various constraints, namely, by the conjugation conditions [4, 8, 10, 15, 17-20, 22-26, 38, 44, 47, 52, 53, 68, 76, 77, 81, 83, 84, 90, 95, 96-100, 112-114, 117, 123].

Boundary Control of PDEs

Author : Miroslav Krstic
Publisher : SIAM
ISBN 13 : 0898718600
Total Pages : 197 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Boundary Control of PDEs by : Miroslav Krstic

Download or read book Boundary Control of PDEs written by Miroslav Krstic and published by SIAM. This book was released on 2008-01-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg-Landau, Schrodinger, Kuramoto-Sivashinsky, KdV, beam, and Navier-Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs.

Computational Optimization of Systems Governed by Partial Differential Equations

Author : Alfio Borzi
Publisher : SIAM
ISBN 13 : 1611972043
Total Pages : 295 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Computational Optimization of Systems Governed by Partial Differential Equations by : Alfio Borzi

Computational Mathematics, Numerical Analysis and Applications

Author : Mariano Mateos
Publisher : Springer
ISBN 13 : 331949631X
Total Pages : 259 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Computational Mathematics, Numerical Analysis and Applications by : Mariano Mateos

Download or read book Computational Mathematics, Numerical Analysis and Applications written by Mariano Mateos and published by Springer. This book was released on 2017-08-03 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this volume gathers the lecture notes of the courses of the “XVII Escuela Hispano-Francesa”, held in Gijón, Spain, in June 2016. Each chapter is devoted to an advanced topic and presents state-of-the-art research in a didactic and self-contained way. Young researchers will find a complete guide to beginning advanced work in fields such as High Performance Computing, Numerical Linear Algebra, Optimal Control of Partial Differential Equations and Quantum Mechanics Simulation, while experts in these areas will find a comprehensive reference guide, including some previously unpublished results, and teachers may find these chapters useful as textbooks in graduate courses. The second part features the extended abstracts of selected research work presented by the students during the School. It highlights new results and applications in Computational Algebra, Fluid Mechanics, Chemical Kinetics and Biomedicine, among others, offering interested researchers a convenient reference guide to these latest advances.

Computational Optimization of Systems Governed by Partial Differential Equations

Author : Alfio Borzi
Publisher : SIAM
ISBN 13 : 9781611972054
Total Pages : 302 pages
Book Rating : 4.9/5 (72 download)

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Book Synopsis Computational Optimization of Systems Governed by Partial Differential Equations by : Alfio Borzi

Download or read book Computational Optimization of Systems Governed by Partial Differential Equations written by Alfio Borzi and published by SIAM. This book was released on 2011-01-01 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book fills a gap between theory-oriented investigations in PDE-constrained optimization and the practical demands made by numerical solutions of PDE optimization problems. The authors discuss computational techniques representing recent developments that result from a combination of modern techniques for the numerical solution of PDEs and for sophisticated optimization schemes. The book offers readers a combined treatment of PDE-constrained optimization and uncertainties and an extensive discussion of multigrid optimization. It provides a bridge between continuous optimization and PDE modeling and focuses on the numerical solution of the corresponding problems.

Optimization and Control for Partial Differential Equations

Author : Roland Herzog
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110695987
Total Pages : 474 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Optimization and Control for Partial Differential Equations by : Roland Herzog

Download or read book Optimization and Control for Partial Differential Equations written by Roland Herzog and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-03-07 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.

Optimal Control Applied to Biological Models

Author : Suzanne Lenhart
Publisher : CRC Press
ISBN 13 : 1420011413
Total Pages : 272 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Optimal Control Applied to Biological Models by : Suzanne Lenhart

Download or read book Optimal Control Applied to Biological Models written by Suzanne Lenhart and published by CRC Press. This book was released on 2007-05-07 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t

Mathematical Control of Coupled PDEs

Author : Irena Lasiecka
Publisher : SIAM
ISBN 13 : 0898714869
Total Pages : 248 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Mathematical Control of Coupled PDEs by : Irena Lasiecka

Download or read book Mathematical Control of Coupled PDEs written by Irena Lasiecka and published by SIAM. This book was released on 2002-01-01 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentrates on systems of hyperbolic and parabolic coupled PDEs that are nonlinear, solve three key problems.

Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems

Author : Irena Lasiecka
Publisher : Cambridge University Press
ISBN 13 : 9780521434089
Total Pages : 678 pages
Book Rating : 4.4/5 (34 download)

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Book Synopsis Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems by : Irena Lasiecka

Download or read book Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems written by Irena Lasiecka and published by Cambridge University Press. This book was released on 2000-02-13 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 2000, this is the first volume of a comprehensive 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. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which is unifying across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 1 includes the abstract parabolic theory for the finite and infinite cases and corresponding PDE illustrations as well as various abstract hyperbolic settings in the finite case. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.

Control of Partial Differential Equations

Author : Giuseppe Da Prato
Publisher : CRC Press
ISBN 13 : 9780824792404
Total Pages : 302 pages
Book Rating : 4.7/5 (924 download)

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Book Synopsis Control of Partial Differential Equations by : Giuseppe Da Prato

Download or read book Control of Partial Differential Equations written by Giuseppe Da Prato and published by CRC Press. This book was released on 1994-08-19 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This useful reference provides recent results as well as entirely new material on control problems for partial differential equations.

Optimization Methods in Partial Differential Equations

Author : Steven Cox
Publisher : American Mathematical Soc.
ISBN 13 : 0821806041
Total Pages : 362 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Optimization Methods in Partial Differential Equations by : Steven Cox

Download or read book Optimization Methods in Partial Differential Equations written by Steven Cox and published by American Mathematical Soc.. This book was released on 1997 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems considered range from basic theoretical issues in the calculus of variations - such as infinite dimensional Hamilton Jacobi equations, saddle point principles, and issues of unique continuation - to ones focusing on application and computation, where theoretical tools are tuned to more specifically defined problems.