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Author : P. J. Hilton
Publisher : Springer
ISBN 13 : 9783540057154
Total Pages : 118 pages
Book Rating : 4.0/5 (571 download)
Download or read book Symposium on Algebraic Topology written by P. J. Hilton and published by Springer. This book was released on 1971-01-01 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jacques Louis Lions
Publisher : Springer
ISBN 13 : 9783642650260
Total Pages : 400 pages
Book Rating : 4.6/5 (52 download)
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-+
Author : Jacques Louis Lions
Publisher : Springer
ISBN 13 : 9783540051152
Total Pages : 400 pages
Book Rating : 4.0/5 (511 download)
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 1971-01-01 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-+
Author : Jacques Louis Lions
Publisher :
ISBN 13 : 9787506215039
Total Pages : 396 pages
Book Rating : 4.2/5 (15 download)
Download or read book Optimal Control of Systems Governed by Partial Differential Equations written by Jacques Louis Lions and published by . This book was released on 1994 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A.K. Aziz
Publisher : Academic Press
ISBN 13 : 1483216306
Total Pages : 289 pages
Book Rating : 4.4/5 (832 download)
Download or read book Control Theory of Systems Governed by Partial Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control Theory of Systems Governed by Partial Differential Equations covers the proceedings of the 1976 Conference by the same title, held at the Naval Surface Weapons Center, Silver Spring, Maryland. The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. This work also presents the principles of the duality and asymptotic methods in control theory, including the variational principle for the heat equation. A chapter highlights systems that are not of the linear quadratic type. This chapter also explores the control of free surfaces and the geometrical control variables. The last chapter provides a summary of the features and applications of the numerical approximation of problems of optimal control. This book will prove useful to mathematicians, engineers, and researchers.
Author : Jacques-Louis Lions
Publisher :
ISBN 13 :
Total Pages : 407 pages
Book Rating : 4.:/5 (859 download)
Download or read book Optimal Control of Systems Governed by Partial Differential Equation written by Jacques-Louis Lions and published by . This book was released on 1971 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tongjia Zheng
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)
Download or read book Optimal Control and Filtering of Systems Governed by Partial Differential Equations written by Tongjia Zheng and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter John Harley
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (111 download)
Download or read book A Survey of Methods for the Optimal Control of Systems Governed by Partial Differential Equations written by Peter John Harley and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alfio Borzi
Publisher : SIAM
ISBN 13 : 1611972043
Total Pages : 295 pages
Book Rating : 4.6/5 (119 download)
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 2012-01-26 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a bridge between continuous optimization and PDE modelling and focuses on the numerical solution of the corresponding problems. Intended for graduate students in PDE-constrained optimization, it is also suitable as an introduction for researchers in scientific computing or optimization.
Author : Andrea Manzoni
Publisher : Springer Nature
ISBN 13 : 3030772268
Total Pages : 507 pages
Book Rating : 4.0/5 (37 download)
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.
Author : Ivan V. Sergienko
Publisher : Springer Science & Business Media
ISBN 13 : 9781402081088
Total Pages : 410 pages
Book Rating : 4.0/5 (81 download)
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].
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Author : Morris, Kirsten
Publisher : National Library of Canada
ISBN 13 :
Total Pages : 87 pages
Book Rating : 4.:/5 (639 download)
Download or read book Time-optimal Control of Systems Governed by Parabolic Partial Differential Equations [microform] : Supremum-norm Problems written by Morris, Kirsten and published by National Library of Canada. This book was released on 1984 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H. Thomas Banks
Publisher : SIAM
ISBN 13 : 9780898713176
Total Pages : 250 pages
Book Rating : 4.7/5 (131 download)
Download or read book Identification and Control in Systems Governed by Partial Differential Equations written by H. Thomas Banks and published by SIAM. This book was released on 1993-01-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fatiha Alabau-Boussouira
Publisher : Springer
ISBN 13 : 3030179494
Total Pages : 276 pages
Book Rating : 4.0/5 (31 download)
Download or read book Trends in Control Theory and Partial Differential Equations written by Fatiha Alabau-Boussouira and published by Springer. This book was released on 2019-07-04 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.
Author : Fredi Tröltzsch
Publisher : American Mathematical Society
ISBN 13 : 1470476444
Total Pages : 417 pages
Book Rating : 4.4/5 (74 download)
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.
Author : Karl Kunisch
Publisher : Springer Science & Business Media
ISBN 13 : 3764389230
Total Pages : 346 pages
Book Rating : 4.7/5 (643 download)
Download or read book Optimal Control of Coupled Systems of Partial Differential Equations written by Karl Kunisch and published by Springer Science & Business Media. This book was released on 2009-12-03 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains contributions originating from the 'Conference on Optimal Control of Coupled Systems of Partial Differential Equations', held at the 'Mathematisches Forschungsinstitut Oberwolfach' in March 2008. This work covers a range of topics such as controllability, optimality systems, model-reduction techniques, and fluid-structure interactions.
Author : Lorenz T. Biegler
Publisher : Springer Science & Business Media
ISBN 13 : 364255508X
Total Pages : 347 pages
Book Rating : 4.6/5 (425 download)
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.
