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  • 1
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    Difference methods for problems with different time scales (1985)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The use of difference methods for weakly nonlinear systems of ordinary differential equations with rapidly oscillating solutions is considered, and a general approach which depends only on the smoothness of the coefficients and the nonlinearities is developed. In particular, one is led to a strategy which is suitable for the detection and resolution of turning points in such systems. A computational example is presented.
    Keywords: NUMERICAL ANALYSIS
    Type: Mathematics of Computation (ISSN 0025-5718); 44; 81-92
    Format: text
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  • 2
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    State and model error estimation for elliptic systems: Applications to large antenna static shape determination (1983)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: This paper outlines the application of various estimation approaches to the problem of static shape determination for large antenna systems. The problem consists of estimating the shape of an antenna surface from measurements of its static deflection. The estimation schemes are based on any one of the modeling options of a single PDE for early insight and understanding, coarse-resolution multiple-PDE models for parametric studies and fine-resolution piecewise-continuum models for detailed design. For any one of these three models, estimator design can be developed using an infinite-dimensional approach, where the necessary finite-element truncation and approximation is conducted after the analytical design has taken place, or it can be based on a finite-dimensional approach, where the model is truncated before the estimation problem is formulated. One of the main objectives of the paper is to develop both approaches while simultaneously investigating their differences and similarities. Simulation results of an application of the finite-dimensional approach to a large parabolic reflector are presented.
    Keywords: NUMERICAL ANALYSIS
    Type: Proc. of the Workshop on Appl. of Distributed System Theory to the Control of Large Space Struct.; p 575-603
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  • 3
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    Kalman-like estimation for static distributed systems Antenna shape from radiation measurements (1985)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: This paper advances an approach to the determination of shape of static distributed systems. It also illustrates the application of the approach to the problems of surface diagnosis of large parabolic reflectors. The estimation methods developed combine in an optimal sense the information from an elliptic model of the structure and from measurements of the structural deflection and of the far-field pattern changes due to the structural deformation. The estimators have a predictor-corrector structure, quite similar to that of a Kalman filter. The system model is first used to obtain a predicted estimate. A correction term is then added to the prediction to obtain the final state estimate. The relative weighting between prediction and correction terms is determined by an estimator gain. As in a Kalman filter, the estimator gain can be expressed in terms of the state estimation error covariance.
    Keywords: CYBERNETICS
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  • 4
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    Numerical Experimentation with Maximum Likelihood Identification in Static Distributed Systems (1985)
    In:  CASI
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    Publication Date: 2016-06-07
    Description: Many important issues in the control of large space structures are intimately related to the fundamental problem of parameter identification. One might also ask how well this identification process can be carried out in the presence of noisy data since no sensor system is perfect. With these considerations in mind the algorithms herein are designed to treat both the case of uncertainties in the modeling and uncertainties in the data. The analytical aspects of maximum likelihood identification are considered in some detail in another paper. The questions relevant to the implementation of these schemes are dealt with, particularly as they apply to models of large space structures. The emphasis is on the influence of the infinite dimensional character of the problem on finite dimensional implementations of the algorithms. Those areas of current and future analysis are highlighted which indicate the interplay between error analysis and possible truncations of the state and parameter spaces.
    Keywords: SPACECRAFT DESIGN, TESTING AND PERFORMANCE
    Type: Proc. of the Workshop on Identification and Control of Flexible Space Struct., Vol. 3; p 377-402
    Format: application/pdf
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  • 5
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    Modeling, estimation and identification methods for static shape determination of flexible structures (1986)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.
    Keywords: SPACECRAFT DESIGN, TESTING AND PERFORMANCE
    Type: AAS PAPER 85-424
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  • 6
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    Static shape control for flexible structures (1986)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: An integrated methodology is described for defining static shape control laws for large flexible structures. The techniques include modeling, identifying and estimating the control laws of distributed systems characterized in terms of infinite dimensional state and parameter spaces. The models are expressed as interconnected elliptic partial differential equations governing a range of static loads, with the capability of analyzing electromagnetic fields around antenna systems. A second-order analysis is carried out for statistical errors, and model parameters are determined by maximizing an appropriate defined likelihood functional which adjusts the model to observational data. The parameter estimates are derived from the conditional mean of the observational data, resulting in a least squares superposition of shape functions obtained from the structural model.
    Keywords: CYBERNETICS
    Type: SAE PAPER 861822
    Format: text
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  • 7
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    Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing (1987)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.
    Keywords: CYBERNETICS
    Type: AIAA PAPER 87-2261
    Format: text
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