Trends In Control Theory And Partial Differential Equations

Author : Fatiha Alabau-Boussouira,Fabio Ancona,Alessio Porretta,Carlo Sinestrari
Publisher : Springer
Page : 276 pages
File Size : 49,5 Mb
Release : 2019-07-04
Category : Mathematics
ISBN : 9783030179496

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Trends in Control Theory and Partial Differential Equations by Fatiha Alabau-Boussouira,Fabio Ancona,Alessio Porretta,Carlo Sinestrari Pdf

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 : J. F. Pommaret
Publisher : Springer Science & Business Media
Page : 578 pages
File Size : 55,9 Mb
Release : 2001
Category : Mathematics
ISBN : 079237035X

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Partial Differential Control Theory by J. F. Pommaret Pdf

Algebraic analysis, that is the algebraic study of systems of partial differential equations by means of module theory and homological algebra, was pioneered around 1970 by M. Kashiwara, B. Malgrange, and V.P. Palamodov. The theory of differential modules, namely modules over a noncommutative ring of differential operators, is a fashionable subject of research today. However, despite its fundamental importance in mathematics, it can only be found in specialist books and papers, and has only been applied in control theory since 1990. This book provides an account of algebraic analysis and its application to control systems defined by partial differential equations. The first volume presents the mathematical tools needed from both commutative algebra, homological algebra, differential geometry and differential algebra. The second volume applies these new methods in order to study the structural and input/output properties of both linear and nonlinear control systems. Hundreds of explicit examples allow the reader to gain insight and experience in these topics.

Author : A.K. Aziz,J.W. Wingate,M.J. Balas
Publisher : Academic Press
Page : 288 pages
File Size : 52,6 Mb
Release : 2014-05-10
Category : Technology & Engineering
ISBN : 9781483216300

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Control Theory of Systems Governed by Partial Differential Equations by A.K. Aziz,J.W. Wingate,M.J. Balas Pdf

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 : Irena Lasiecka,Roberto Triggiani
Publisher : Unknown
Page : 128 pages
File Size : 50,6 Mb
Release : 2014-02-20
Category : Electronic
ISBN : 1299748929

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Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-Like Systems Over a Finite Time Horizon by Irena Lasiecka,Roberto Triggiani Pdf

Second of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations.

Author : Irena Lasiecka
Publisher : SIAM
Page : 248 pages
File Size : 50,9 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 9780898714869

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Mathematical Control of Coupled PDEs by Irena Lasiecka Pdf

Concentrates on systems of hyperbolic and parabolic coupled PDEs that are nonlinear, solve three key problems.

Author : Jean-michel Coron,Tatsien Li,Zhiqiang Wang
Publisher : World Scientific
Page : 315 pages
File Size : 46,7 Mb
Release : 2023-04-11
Category : Mathematics
ISBN : 9789811271649

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Control Of Partial Differential Equations by Jean-michel Coron,Tatsien Li,Zhiqiang Wang Pdf

This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.

Author : Qi Lü,Xu Zhang
Publisher : Springer Nature
Page : 592 pages
File Size : 46,6 Mb
Release : 2021-10-19
Category : Science
ISBN : 9783030823313

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Mathematical Control Theory for Stochastic Partial Differential Equations by Qi Lü,Xu Zhang Pdf

This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Author : Guenter Leugering,Oleg Imanuvilov,Bing-Yu Zhang,Roberto Triggiani
Publisher : CRC Press
Page : 416 pages
File Size : 41,6 Mb
Release : 2005-05-27
Category : Mathematics
ISBN : 9781420028317

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Control Theory of Partial Differential Equations by Guenter Leugering,Oleg Imanuvilov,Bing-Yu Zhang,Roberto Triggiani Pdf

The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids a

Author : J. F. Pommaret
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 47,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0792370368

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Partial Differential Control Theory by J. F. Pommaret Pdf

Author : Irena Lasiecka,Roberto Triggiani
Publisher : Cambridge University Press
Page : 458 pages
File Size : 41,7 Mb
Release : 2000-02-13
Category : Mathematics
ISBN : 0521584019

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Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems Over a Finite Time Horizon by Irena Lasiecka,Roberto Triggiani Pdf

Second of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations.

Author : A. Anzaldo-Meneses
Publisher : World Scientific
Page : 495 pages
File Size : 48,7 Mb
Release : 2002
Category : Mathematics
ISBN : 9789810248413

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Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications by A. Anzaldo-Meneses Pdf

Concerns contemporary trends in nonlinear geometric control theory and its applications.

Author : Irena Lasiecka,Roberto Triggiani
Publisher : Unknown
Page : 128 pages
File Size : 51,9 Mb
Release : 2013-08-13
Category : Electronic
ISBN : 1299749216

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Control Theory for Partial Differential Equations by Irena Lasiecka,Roberto Triggiani Pdf

First of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations, originally published in 2000.

Author : Irena Lasiecka,Roberto Triggiani
Publisher : Cambridge University Press
Page : 678 pages
File Size : 51,9 Mb
Release : 2000-02-13
Category : Mathematics
ISBN : 0521434084

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Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems by Irena Lasiecka,Roberto Triggiani Pdf

First of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations, originally published in 2000.

Author : Irena Lasiecka,Roberto Triggiani
Publisher : Cambridge University Press
Page : 0 pages
File Size : 44,6 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 0521155673

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Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems by Irena Lasiecka,Roberto Triggiani Pdf

This is the first volume of a comprehensive and up-to-date 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. The authors describe both continuous theory and numerical approximation. They use an abstract space, operator theoretic approach, based on semigroups methods and 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 I includes the abstract parabolic theory (continuous theory and numerical approximation theory) for the finite and infinite cases and corresponding PDE illustrations, and presents numerous new 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.

Author : Peter I. Kogut,Günter R. Leugering
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 41,8 Mb
Release : 2011-09-09
Category : Science
ISBN : 9780817681494

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Optimal Control Problems for Partial Differential Equations on Reticulated Domains by Peter I. Kogut,Günter R. Leugering Pdf

In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains.