Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems Over a Finite Time Horizon

Continuous and Approximation Theories
Author: Irena Lasiecka,Roberto Triggiani
Publisher: Cambridge University Press
ISBN: 9780521584012
Category: Mathematics
Page: 1067
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Originally published in 2000, this is the second 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 unifies 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 2 is focused on the optimal control problem over a finite time interval for hyperbolic dynamical systems. A few abstract models are considered, each motivated by a particular canonical hyperbolic dynamics. 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.

Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation

Author: Weijiu Liu
Publisher: Springer Science & Business Media
ISBN: 9783642046131
Category: Mathematics
Page: 296
View: 2645

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Unlike abstract approaches to advanced control theory, this volume presents key concepts through concrete examples. Once the basic fundamentals are established, readers can apply them to solve other control problems of partial differential equations.

Differential Geometric Methods in the Control of Partial Differential Equations

1999 AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations, University of Colorado, Boulder, June 27-July 1, 1999
Author: Robert Gulliver,Walter Littman,Roberto Triggiani
Publisher: American Mathematical Soc.
ISBN: 0821819275
Category: Mathematics
Page: 406
View: 8331

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This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on ``Differential Geometric Methods in the Control of Partial Differential Equations'', which was held at the University of Colorado in Boulder in June 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable coefficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has been long established, for at least 30 years, between differential geometry and control of ordinary differential equations, a comparable relationship between differential geometry and control of partial differential equations (PDEs) is a new and promising topic. Very recent research, just prior to the Colorado conference, supported the expectation that differential geometric methods, when brought to bear on classes of PDE modelling and control problems with variable coefficients, will yield significant mathematical advances. The papers included in this volume--written by specialists in PDEs and control of PDEs as well as by geometers--collectively support the claim that the aims of the conference are being fulfilled. In particular, they endorse the belief that both subjects--differential geometry and control of PDEs--have much to gain by closer interaction with one another. Consequently, further research activities in this area are bound to grow.

Control of Partial Differential Equations

Cetraro, Italy 2010, Editors: Piermarco Cannarsa, Jean-Michel Coron
Author: Fatiha Alabau-Boussouira,Roger Brockett,Olivier Glass,Jérôme Le Rousseau,Enrique Zuazua
Publisher: Springer
ISBN: 3642278930
Category: Mathematics
Page: 344
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The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010. Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a friendly introduction to, and an updated account of, some of the most active trends in current research.

Current Trends In Operator Theory And Its Applications

Author: Joseph A. Ball
Publisher: Springer Science & Business Media
ISBN: 9783764370671
Category: Language Arts & Disciplines
Page: 595
View: 9784

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Many developments on the cutting edge of research in operator theory and its applications, and related areas of mathematics, are reflected in this collection of original and review articles. Particular emphasis lies on the applications of operator theory to basic problems in distributed parameter systems, mathematical physics, wavelets, and numerical analysis.Review articles include a report on recent achievements and future directions of research in the area of operator theory and its diverse applications.The intended audience is researchers and graduate students in mathematics, physics, and electrical engineering.

Control Theory of Partial Differential Equations

Author: Guenter Leugering,Oleg Imanuvilov,Bing-Yu Zhang,Roberto Triggiani
Publisher: CRC Press
ISBN: 1420028316
Category: Mathematics
Page: 416
View: 3234

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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 and elastic structures, and fluid dynamics and the new challenges that they present. Other control theoretic problems include parabolic systems, dynamical Lame systems, linear and nonlinear hyperbolic equations, and pseudo-differential operators on a manifold. This is a valuable tool authored by international specialists in the field.


Author: N.A
Publisher: N.A
Category: American literature
Page: N.A
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Its Content, Methods and Meaning
Author: A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev
Publisher: Courier Corporation
ISBN: 0486157873
Category: Mathematics
Page: 1120
View: 2790

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Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

Stability and Stabilization of Infinite Dimensional Systems with Applications

Author: Zheng-Hua Luo,Bao-Zhu Guo,Ömer Morgül
Publisher: Springer Science & Business Media
ISBN: 1447104196
Category: Computers
Page: 403
View: 8703

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This book reports on recent achievements in stability and feedback stabilization of infinite systems. In particular emphasis is placed on second order partial differential equations, such as Euler-Bernoulli beam equations, which arise from vibration control of flexible robots arms and large space structures. Various control methods such as sensor feedback control and dynamic boundary control are applied to stabilize the equations. Many new theorems and methods are included in the book. Proof procedures of existing theorems are simplified, and detailed proofs have been given to most theorems. New results on semigroups and their stability are presented, and readers can learn several useful techniques for solving practical engineering problems. Until now, the recently obtained research results included in this book were unavailable in one volume. This self-contained book is an invaluable source of information for all those who are familiar with some basic theorems of functional analysis.

Control and Nonlinearity

Author: Jean-Michel Coron
Publisher: American Mathematical Soc.
ISBN: 0821849182
Category: Commande non linéaire
Page: 426
View: 468

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This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics. The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations.