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: 2101

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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.
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Mathematics of Complexity and Dynamical Systems

Author: Robert A. Meyers

Publisher: Springer Science & Business Media

ISBN: 1461418054

Category: Mathematics

Page: 1858

View: 7262

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Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
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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: AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations,Robert Gulliver,Ams-IMS-Siam Joint Summer Research Conference on Differential Geometric Methods in the Con

Publisher: American Mathematical Soc.

ISBN: 0821819275

Category: Mathematics

Page: 406

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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.
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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.
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Current Trends In Operator Theory And Its Applications

Author: Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman

Publisher: Springer Science & Business Media

ISBN: 9783764370671

Category: Language Arts & Disciplines

Page: 595

View: 5041

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

Continuous and Approximation Theories

Author: Irena Lasiecka,Roberto Triggiani

Publisher: Cambridge University Press

ISBN: 9780521434089

Category: Mathematics

Page: 1067

View: 9656

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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.
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