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Showing 1 to 20 of 75 for “"Taylor Series"”.
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Multi-Input Multi-Output Repetitive Control Theory And Taylor Series Based Repetitive Control Design
… This dissertation presents a new approach using Taylor Series Expansion of the inverse system z-transfer function model to design Finite Impulse Response (FIR) repetitive controllers for single-input single-output (SISO) systems, and compares the designs obtained to those generated by …
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A new numerical optimization method based on Taylor series for challenging trajectory optimization problems
… of the new methods they are tested on a series of progressively more challenging optimal control problems, culminating in the capstone problem. This capstone problem is a low-thrust Earth-Moon transfer that uses the interesting dynamics of the circular restricted three body problem …
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POLARIZATION ABERRATIONS
… Fresnel equations and thin film equations into a Taylor series. Methods are given for calculating the Taylor series coefficients for a multilayer coated interface whose polarization performance is known, for example from a thin film design program. Equations are derived for the propagation of …
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DEVELOPMENT OF HIGH-ORDER FINITE VOLUME METHODS ON UNSTRUCTURED GRIDS AND THEIR APPLICATIONS
… volume method, a high-order polynomial based on Taylor series expansion is constructed within every control cell to approximate the solution function. The unknown coefficients in the Taylor series expansion, i.e., the various derivatives, are approximated by the functional values at the cell …
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The functionality of spatial and time domain artificial neural models.
… and introduces a new neural model, termed a Taylor Series neuron. This is designed to be flexible enough to assume most mathematical functions. The unit is based on Power Series theory and a specifically implemented Taylor Series neuron is demonstrated. These neurons are of particular …
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UMVU estimation of phase and group delay with small samples
Group delay between two univariate time series is a measure, in units of time, of how one series leads or lags the other at specific frequencies. The only published method of estimating group delay is Hannan and Thomson (1973); however, their method is highly asymptotic and does not allow inference …
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ΧΑΡΑΚΤΗΡΙΣΜΟΣ ΔΥΝΑΜΟΣΕΙΡΩΝ ΜΕ ΜΕΡΙΚΑ ΑΘΡΟΙΣΜΑΤΑ ΠΑΝΩ ΣΕ ΠΕΠΕΡΑΣΜΕΝΟ ΠΛΗΘΟΣ ΚΥΚΛΩΝ
LET K BE THE CLASS OF TRIGONOMETRIC SERIES OF POWER TYPE, I.E. TAYLOR SERIES Σ C ZN FOR Z=E IX, WHOSE PARTIAL SUMS FOR ALL X IN E, WHERE E IS A NONDENUMERABLESUBSET OF (0,2Π) LIE ON A FINITE NUMBER OF CIRCLES (A PRIORI DEPENDINGON X) IN THE COMPLEX PLANE. THE MAIN RESULT OF THIS PAPER IS THAT FOR …
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Algebraic structures in stochastic differential equations
… obtained by truncating the stochastic Taylor series. In doing so we generalize recent results concerning stochastic differential equations driven by Wiener processes. The aforementioned works studied integration schemes obtained by applying an invertible mapping to the stochastic Taylor …
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Elementos finitos Taylorianos
A finite element model which makes use of the Taylor series to represent the displacement field, is presented. This way the interpolation functions for a domain in the periphery of the origin of the expansion in series are defined in respect to some points in the periphery of that origin. The form …
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Contributions to the Theory of Q-Series and Mock Theta Functions
In Chapter 2, we prove, for the first time, a series of four related identities from Ramanujan's lost notebook. These are one-parameter identities which would directly imply some of the relations for the third order mock theta functions given by Ramanujan. In Chapter 3, we prove very general …
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An extension to thin aerofoil theory obtained by using eulerlets and oseenlets
… mathematicalrepresentation is achieved, then the Taylor series approximation is applied assuming athin aerofoil body. The first term in the approximation yields standard thin aerofoiltheory, and additionally we give the next three terms in the approximation with theirorders of magnitude.
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The field of reals with Gevrey functions is model complete and o-minimal
… in $\IR\sb{\cal G},$ as are all functions whose Taylor series expansion at the origin is multisummable in the direction $\IR\sp+$.
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Large eddy simulation of compressible channel flow
… the filtering procedure are modeled based on a Taylor series expansion. The subgrid scale Reynolds terms are modeled using a compressible extension of an existing incompressible model for wall bounded flows. The equations are solved numerically using a modified four-step Runge-Kutta procedure in …
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Transient analyses of viscoelastic materials with applications to numerical models
… of the equation of motion in the form of a Taylor series. This Taylor series, in combination with a Leibniz integral rule, provides a faster approach to approximating viscoelastic behavior for some problems. The third part considers non-monotonic relaxation functions. While it is generally …
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An accuracy study of central finite difference methods in second order boundary value problems
… the error in each method are obtained by using Taylor series to derive the differential equations which exactly represent the finite difference approximations. The resulting differential equations are accurately solved by a perturbation technique which yields the error directly. A half station …
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Semiparametric Techniques for Response Surface Methodology
… optimize products and processes. A second-order Taylor series approximation is commonly utilized to model the data; however, parametric models are not always adequate. In these situations, any degree of model misspecification may result in serious bias of the estimated response. Nonparametric …
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Two step runge-KUTTA-nystrom method for solving second-order ordinary differential equations
… conditions of TSRK method were obtained by using Taylor series expansion. The explicit TSRK method was derived and its stability were investigated. It was then analyzed experimentally. The numerical results obtained were analyzed by making comparisons with the existing methods in terms of maximum …
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Second-Order Relative Motion Equations
… orbit in spherical coordinates are expanded in Taylor series form using reference conditions consistent with that of a circular orbit. Only terms that are linear or quadratic in state variables are kept in the expansion. A perturbation method is employed to obtain an approximate solution of the …
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Integration of quality-by-design into control systems design for continuous pharmaceutical manufacturing
… the mapping between CPPs and CQAs using a Taylor series. The full design space can then be calculated using a plantwide approach or a unit-by-unit approach. Common inner approximations of the design space (e.g. hyper-rectangles) can result in significant conservatism, especially when a …
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Numerical Estimation of L2 Gain for Nonlinear Input-Output Systems
… class of Hamilton-Jacobi-Bellman equations via a Taylor series-based approximation, which is scalable to high-dimensional problems given the utilization of linear tensor systems. The ideas are demonstrated through a few concrete examples that include a one-dimensional problem with an explicit …
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