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...

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

Author: H. T. Banks

Publisher:

Published: 1988

Total Pages: 74

ISBN-13:

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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 infinite 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. Keywords: Nonlinear distributed systems; Numerical analysis; Inverse problems; Approximation. (jhd).

Approximation Theory and Computational Methods for the Identification and Control of Distributed Parameter Systems
Approximation Theory and Computational Methods for the Identification and Control of Distributed Parameter Systems

Author:

Publisher:

Published: 1993

Total Pages: 15

ISBN-13:

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A brief overview and summary of the research carried out in the area of approximation theory and computational methods for the identification and control of distributed parameter systems is provided. In particular, this final report details our efforts during the period 1 November 1990-31 October, 1993 on projects involving the adaptive control and estimation, ana on-line identification of distributed parameter systems (including a collaborative experimental-effort with Air Force personnel at Phillips Laboratory at Edwards Air Force Base), the identification and control of degenerate distributed parameter systems, Multi-grid methods for the solution of optimal LQR control problems for infinite dimensional systems, wavelet based approximation in the optimal LQ control of distributed parameter systems, the identification of nonlinear Volterra equations with application to materials with memory, the LQ control of linear and nonlinear distributed parameter systems with infinite spatial domain, and optimal control and estimation of thermoelastic systems with applications to thermo-acoustic refrigeration. Approximation control, Identification distributed parameter systems.

Approximation Methods for the Identification and Control of Distributed Parameter Systems with Applications to Flexible Structures
Approximation Methods for the Identification and Control of Distributed Parameter Systems with Applications to Flexible Structures

Author:

Publisher:

Published: 1991

Total Pages: 14

ISBN-13:

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A brief overview and summary of results obtained in the development, analysis, and testing of approximation theory and techniques for the identification and control of distributed parameter systems is provided. The research carried out under this grant can be classified into seven sub-headings. These include (1) the identification of nonlinear distributed parameter systems, (2) the identification and control of thermoelastic systems, (3) the identification and control of degenerate distributed parameter systems, (4) discrete-time linear quadratic control of distributed parameter systems, (5) optimal LQG control of discrete time parabolic systems, (6) optimal fixed finite order compensators for infinite dimensional systems, and (7) convergence of Galerkin approximations to operator Riccati equations. Our results in each of these areas is described separately and in turn.

Optimal Measurement Methods for Distributed Parameter System Identification
Optimal Measurement Methods for Distributed Parameter System Identification

Author: Dariusz Ucinski

Publisher: CRC Press

Published: 2004-08-27

Total Pages: 392

ISBN-13: 0203026780

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For dynamic distributed systems modeled by partial differential equations, existing methods of sensor location in parameter estimation experiments are either limited to one-dimensional spatial domains or require large investments in software systems. With the expense of scanning and moving sensors, optimal placement presents a critical problem.

Framework for Analysis and Identification of Nonlinear Distributed Parameter Systems using Bayesian Uncertainty Quantification based on Generalized Polynomial Chaos
Framework for Analysis and Identification of Nonlinear Distributed Parameter Systems using Bayesian Uncertainty Quantification based on Generalized Polynomial Chaos

Author: Janya-anurak, Chettapong

Publisher: KIT Scientific Publishing

Published: 2017-04-04

Total Pages: 248

ISBN-13: 3731506424

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In this work, the Uncertainty Quantification (UQ) approaches combined systematically to analyze and identify systems. The generalized Polynomial Chaos (gPC) expansion is applied to reduce the computational effort. The framework using gPC based on Bayesian UQ proposed in this work is capable of analyzing the system systematically and reducing the disagreement between the model predictions and the measurements of the real processes to fulfill user defined performance criteria.