An Approximation Theory for the Identification of Nonlinear Distributed Parameter Systems
An Approximation Theory for the Identification of Nonlinear Distributed Parameter Systems

Author: National Aeronautics and Space Administration (NASA)

Publisher: Createspace Independent Publishing Platform

Published: 2018-06-30

Total Pages: 38

ISBN-13: 9781722063559

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An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed. Banks, H. T. and Reich, Simeon and Rosen, I. G. Langley Research Center NAS1-18107; NAG1-517; RTOP 505-90-21-01...

Control of Distributed Parameter Systems 1989
Control of Distributed Parameter Systems 1989

Author: M. Amouroux

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 533

ISBN-13: 1483298817

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This volume presents state-of-the-art reports on the theory, and current and future applications of control of distributed parameter systems. The papers cover the progress not only in traditional methodology and pure research in control theory, but also the rapid growth of its importance for different applications. This title will be of interest to researchers working in the areas of mathematics, automatic control, computer science and engineering.

Estimation Techniques for Distributed Parameter Systems
Estimation Techniques for Distributed Parameter Systems

Author: H.T. Banks

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 328

ISBN-13: 1461237009

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The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations. Our attempts to apply control theory techniques to such prob lems in several areas of science convinced us that in the need for better and more detailed models of distributed/ continuum processes in biology and mechanics lay a rich, interesting, and challenging class of fundamen tal questions. These questions, which involve science and mathematics, are typical of those arising in inverse or parameter estimation problems. Our efforts on inverse problems for distributed parameter systems, which are infinite dimensional in the most common realizations, began about seven years ago at a time when rapid advances in computing capabilities and availability held promise for significant progress in the development of a practically useful as well as theoretically sound methodology for such problems. Much of the research reported in our presentation was not begun when we outlined the plans for this monograph some years ago. By publishing this monograph now, when only a part of the originally intended topics are covered (see Chapter VII in this respect), we hope to stimulate the research and interest of others in an area of scientific en deavor which has exceeded even our optimistic expectations with respect to excitement, opportunity, and stimulation. The computer revolution alluded to above and the development of new codes allow one to solve rather routinely certain estimation problems that would have been out of the question ten years ago.

Systems Approaches in Computer Science and Mathematics
Systems Approaches in Computer Science and Mathematics

Author: G.E. Lasker

Publisher: Elsevier

Published: 2014-05-20

Total Pages: 693

ISBN-13: 1483149811

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Applied Systems and Cybernetics, Volume V: Systems Approaches in Computer Science and Mathematics covers the proceedings of the International Congress on Applied Systems Research and Cybernetics. This book discusses trends and advances in the application of systems science and cybernetics to various fields. This volume reviews the systems approaches in computer science and mathematics and concentrates on several major areas of systems research in computer science and theoretical and applied mathematics. This book will be of great interest to computer scientists interested in the development of the theories and applications of computer science.

Research Directions in Distributed Parameter Systems
Research Directions in Distributed Parameter Systems

Author: Ralph C. Smith

Publisher: SIAM

Published: 2003-01-01

Total Pages: 283

ISBN-13: 0898715482

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Eleven chapters, written by experts in their respective fields, on topics ranging from control of the Navier-Stokes equations to nondestructive evaluation - all of which are modeled by distributed parameter systems.

Spatio-Temporal Modeling of Nonlinear Distributed Parameter Systems
Spatio-Temporal Modeling of Nonlinear Distributed Parameter Systems

Author: Han-Xiong Li

Publisher: Springer Science & Business Media

Published: 2011-02-24

Total Pages: 175

ISBN-13: 940070741X

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The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein systems and their identifi cation methods. Then, the traditional Volterra model is extended to DPS, which results in the spatio-temporal Volterra model and its identification algorithm. All these methods are based on linear time/space separation. Sometimes, the nonlinear time/space separation can play a better role in modeling of very complex processes. Thus, a nonlinear time/space separation based neural modeling is also presented for a class of DPS with more complicated dynamics. Finally, all these modeling approaches are successfully applied to industrial thermal processes, including a catalytic rod, a packed-bed reactor and a snap curing oven. The work is presented giving a unifi ed view from time/space separation. The book also illustrates applications to thermal processes in the electronics packaging and chemical industry. This volume assumes a basic knowledge about distributed parameter systems, system modeling and identifi cation. It is intended for researchers, graduate students and engineers interested in distributed parameter systems, nonlinear systems, and process modeling and control.