Optimal control with Chebyshev minimax performance index.
Optimal control of dynamic systems with minimax type performance index, discussing application of proposed method of solution
OPTIMAL CONTROL↗
SEARCH · Search NASA
Results for “function approximation”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Error analysis for a chopper-modulated infrared detection system.
Chopper modulated IR detection system error analysis through minimizing mean square error of approximating output function
Manwell, T.↗
An algorithm for interpolation and numerical differentiation
Easily automated technique for computing continuous function to approximate discrete set of data
Engvall, J. L.↗
A noniterative method of obtaining Tchebycheff rational approximations
Noniterative method of obtaining rational forms as approximations to functions for power series expressions using Tchebycheff polynomial properties for improving accuracy
Hagar, H., Jr.↗
Techniques of orbital decay and long-term ephemeris prediction for satellites in earth orbit
In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.
Barry, B. F.↗
Energy distribution functions of kilovolt ions parallel and perpendicular to the magnetic field of a modified Penning discharge
The distribution function of ion energy parallel to the magnetic field of a modified Penning discharge has been measured with a retarding potential energy analyzer. These ions escaped through one of the throats of the magnetic mirror geometry. Simultaneous measurements of the ion energy distribution function perpendicular to the magnetic field have been made with a charge exchange neutral detector. The ion energy distribution functions are approximately Maxwellian, and the parallel and perpendicular kinetic temperatures are equal within experimental error. These results suggest that turbulent processes previously observed in this discharge Maxwellianize the velocity distribution along a radius in velocity space and cause an isotropic energy distribution. When the distributions depart from Maxwellian, they are enhanced above the Maxwellian tail.
Roth, R. J.↗
The new variable BD plus 60 deg 2633
The star BD + 60 deg 2633 is reported to be variable. Observations and light distribution function as well as the analytical approximation of this function are given.
Lukatskaya, F. I.↗
Energy distribution functions of kilovolt ions in a modified Penning discharge.
The distribution function of ion energy parallel to the magnetic field of a modified Penning discharge has been measured with a retarding potential energy analyzer. These ions escaped through one of the throats of the magnetic mirror geometry. Simultaneous measurements of the ion energy distribution function perpendicular to the magnetic field have been made with a charge-exchange neutral detector. The ion energy distribution functions are approximately Maxwellian, and the parallel and perpendicular kinetic temperatures are equal within experimental error. These results suggest that turbulent processes previously observed in this discharge Maxwellianize the velocity distribution along a radius in velocity space, and result in an isotropic energy distribution.
Roth, J. R.↗
Energy distribution functions of kilovolt ions in a modified Penning discharge.
The distribution function of ion energy parallel to the magnetic field of a modified Penning discharge has been measured with a retarding potential energy analyzer. These ions escaped through one of the throats of the magnetic mirror geometry. Simultaneous measurements of the ion energy distribution function perpendicular to the magnetic field have been made with a charge-exchange neutral detector. The ion energy distribution functions are approximately Maxwellian, and the parallel and perpendicular kinetic temperatures are equal within experimental error. These results suggest that turbulent processes previously observed in this discharge Maxwellianize the velocity distribution along a radius in velocity space, and result in an isotropic energy distribution.
Roth, J. R.↗
Aplanatic two-mirror telescopes: A systematic study. I - Cassegrainian configuration
A systematic performance analysis of aplanatic Cassegrainian telescopes has been accomplished by means of a ray trace program. The results indicate that the available field angle for a given geometric spot size is, to a very close approximation, a function of the relative back focal distance only. Image curvatures, as computed by third-order theory and by the ray trace program, were found to be in very close agreement. Image curvature is plotted as a function of the ray height ratio for a wide range of secondary magnification.
Wyman, C. L.↗
Algorithms
The implementation of the algorithms used in the flight program to approximate elementary functions and mathematical procedures was checked. This was done by verifying that at least one, and in most cases, more than one function computed through the use of the algorithms was calculated properly. The following algorithms were checked: sine-cosine, arctangent, natural logarithm, square root, inverse square root, as well as the vector dot and cross products.
Source record↗
The calculation of theoretical chromospheric models and predicted OSO 1 spectra
Theoretical solar chromospheric and photospheric models are computed for use in analyzing OSO 8 spectra. The Vernazza, Avrett, and Loeser (1976) solar model is updated and self-consistent non-LTE number densities for H I, He I, He II, C I, Mg I, Al I, Si I, and H(-) are produced. These number densities are used in the calculation of a theoretical solar spectrum from 90 to 250 nm, including approximately 7000 lines in non-LTE. More than 60,000 lines of other elements are treated with approximate source functions.
Avrett, E. H.↗
Thermionic work function of /Cs/ZnO
The collector electrode of a thermionic converter requires a material having a low thermionic work function and chemical stability in a Cs atmosphere in the 800-K range. This letter reports that ZnO with an adsorbed Cs film meets these requirements. The work function is approximately 1.3 eV. Various methods of preparing the ZnO film are described as well as an experiment in which Cs was replaced by K.
Sommer, A. H.↗
Power law relationships for rain attenuation and reflectivity
The equivalent reflectivity, specific attenuation and volumetric backscatter cross section of rain are calculated and tabulated at a number of frequencies from 1 to 500 GHz using classical Mie theory. The first two parameters are shown to be closely approximated as functions of rain rate by the power law aR to the b power. The a's and b's are also tabulated and plotted for convenient reference.
Devasirvatham, D. M. J.↗
An analytical technique for predicting the characteristics of a flexible wing equipped with an active flutter-suppression system and comparison with wind-tunnel data
An analytical technique for predicting the performance of an active flutter-suppression system is presented. This technique is based on the use of an interpolating function to approximate the unsteady aerodynamics. The resulting equations are formulated in terms of linear, ordinary differential equations with constant coefficients. This technique is then applied to an aeroelastic model wing equipped with an active flutter-suppression system. Comparisons between wind-tunnel data and analysis are presented for the wing both with and without active flutter suppression. Results indicate that the wing flutter characteristics without flutter suppression can be predicted very well but that a more adequate model of wind-tunnel turbulence is required when the active flutter-suppression system is used.
Abel, I.↗
A cubic extended interior penalty function for structural optimization
This paper describes an optimization procedure for the minimum weight design of complex structures. The procedure is based on a new cubic extended interior penalty function (CEIPF) used with the sequence of unconstrained minimization technique (SUMT) and Newton's method. The Hessian matrix of the penalty function is approximated using only constraints and their derivatives. The CEIPF is designed to minimize the error in the approximation of the Hessian matrix, and as a result the number of structural analyses required is small and independent of the number of design variables. Three example problems are reported. The number of structural analyses is reduced by as much as 50 per cent below previously reported results.
Prasad, B.↗
Accelerator test of the coded aperture mask technique for gamma-ray astronomy
A prototype gamma-ray telescope employing the coded aperture mask technique has been constructed and its response to a point source of 20 MeV gamma-rays has been measured. The point spread function is approximately a Gaussian with a standard deviation of 12 arc minutes. This resolution is consistent with the cell size of the mask used and the spatial resolution of the detector. In the context of the present experiment, the error radius of the source position (90 percent confidence level) is 6.1 arc minutes.
Jenkins, T. L.↗
Computational methods for estimation of parameters in hyperbolic systems
Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.
Banks, H. T.↗