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Exponential Convergence (exponential + convergence)

Distribution by Scientific Domains
Engineering70%
Mathematics and Statistics20%
Distribution within Engineering
Control Systems Technology71%
Numerical Methods & Algorithms28%

Kinds of Exponential Convergence

  • global exponential convergence
    		•

    Selected Abstracts

    Rapid Exponential Convergence of Finite Element Estimates of the Effective Properties of Heterogeneous Materials

    ADVANCED ENGINEERING MATERIALS, Issue 11 2007
    A. Gusev
    We develop and validate a general-purpose error estimator for the finite element solutions for the effective properties of heterogeneous materials. We show that the error should decrease exponentially upon increasing order of the polynomial interpolation. We use this finding to demonstrate the practical feasibility of reliable property predictions for a majority of particulate-morphology heterogeneous materials. [source]

    Exponential convergence of the Kalman filter based parameter estimation algorithm

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2003
    Liyu Cao
    Abstract In this paper we shall present a new method to analyse the convergence property of the Kalman filter based parameter estimation algorithms. This method for convergence analysis is mainly based on some matrix inequalities and is more simple than some of the existing approaches in the literature. This method can simultaneously provide both lower and upper bounds on the exponential convergence rate as the functions of bounds of the related matrices, such as the covariance matrices. A simulation example is provided to illustrate the convergence property of the Kalman filter based algorithms. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    On solving the cracked-beam problem by block method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008
    A. A. Dosiyev
    Abstract An extremely accurate solution is obtained for the cracked-beam problem by one-block version of the block method (BM). The obtained numerical results demonstrate the exponential convergence of the BM with respect to the number of quadrature nodes. A simple and high accurate formula to compute the stress intensity factor is given. The comparisons with other high accurate results in the literature have been carried out. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    A pseudospectral Fourier method for a 1D incompressible two-fluid model

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2008
    H. Holmås
    Abstract This paper presents an accurate and efficient pseudospectral (PS) Fourier method for a standard 1D incompressible two-fluid model. To the knowledge of the authors, it is the first PS method developed for the purpose of modelling waves in multiphase pipe flow. Contrary to conventional numerical methods, the PS method combines high accuracy and low computational costs with flexibility in terms of handling higher order derivatives and different types of partial differential equations. In an effort to improve the description of the stratified wavy flow regime, it can thus serve as a valuable tool for testing out new two-fluid model formulations. The main part of the algorithm is based on mathematical reformulations of the governing equations combined with extensive use of fast Fourier transforms. All the linear operations, including differentiations, are performed in Fourier space, whereas the nonlinear computations are performed in physical space. Furthermore, by exploiting the concept of an integrating factor, all linear parts of the problem are integrated analytically. The remaining nonlinear parts are advanced in time using a Runge,Kutta solver with an adaptive time step control. As demonstrated in the results section, these steps in sum yield a very accurate, fast and stable numerical method. A grid refinement analysis is used to compare the spatial convergence with the convergence rates of finite difference (FD) methods of up to order six. It is clear that the exponential convergence of the PS method is by far superior to the algebraic convergence of the FD schemes. Combined with the fact that the scheme is unconditionally linearly stable, the resulting increase in accuracy opens for several orders of magnitude savings in computational time. Finally, simulations of small amplitude, long wavelength sinusoidal waves are presented to illustrate the remarkable ability of the PS method to reproduce the linear stability properties of the two-fluid model. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    A nonlinear adaptive speed tracking control for sensorless permanent magnet step motors with unknown load torque

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2008
    P. Tomei
    Abstract Assuming that only stator currents and voltages are available for feedback, a nonlinear adaptive speed tracking control algorithm is proposed for a permanent magnet step motor with unknown constant load torque. It relies on three new theoretical results: the ,s-alignment' and ,c-alignment' procedures, in which the motor is forced to reach certain known equilibrium points, and an output feedback controller which guarantees asymptotic speed tracking for every initial condition belonging to an explicitly computed domain of attraction (global exponential convergence is achieved in the case of known constant load torque). Numerical simulation results illustrate the effectiveness of the proposed solution. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Robust discontinuous exponential regulation of dynamic nonholonomic wheeled mobile robots with parameter uncertainties

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2008
    B. L. Ma
    Abstract For regulating a dynamic nonholonomic WMR (wheeled mobile robot) with parameter uncertainties, we derive a simple robust discontinuous control law, yielding a global exponential convergence of position and orientation to the desired set point despite parameter uncertainties. The controller design relies on separating the error dynamics into two subsystems, followed by robust feedback control laws to stabilize the subsystems. The effectiveness of the proposed control laws is verified by simulation. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Chattering-free sliding mode control for a class of nonlinear mechanical systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2001
    Vicente Parra-Vega
    Abstract Second-order sliding mode control (2-smc) and dynamic sliding mode control (dsmc) eliminate the disturbing characteristic of chattering in static sliding mode control under the assumption that the derivative of the sliding surface is available or complex inequalities at the acceleration level can be constructed. In this paper, passivity-based adaptive and non-adaptive chattering-free sliding mode controllers are proposed assuming that the upper bound of the norm of the derivative of the sliding surface is available, a weaker and easy to implement assumption in comparison to those of 2-smc and dsmc. The closed-loop system accounts explicitly for the invariance condition without reaching phase, and therefore for a desired transient response with global exponential convergence of tracking errors. Preliminary experiments are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Null-field approach for Laplace problems with circular boundaries using degenerate kernels

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2009
    Jeng-Tzong Chen
    Abstract In this article, a semi-analytical method for solving the Laplace problems with circular boundaries using the null-field integral equation is proposed. The main gain of using the degenerate kernels is to avoid calculating the principal values. To fully utilize the geometry of circular boundary, degenerate kernels for the fundamental solution and Fourier series for boundary densities are incorporated into the null-field integral equation. An adaptive observer system is considered to fully employ the property of degenerate kernels in the polar coordinates. A linear algebraic system is obtained without boundary discretization. By matching the boundary condition, the unknown coefficients can be determined. The present method can be seen as one kind of semianalytical approaches since error only attributes to the truncated Fourier series. For the eccentric case, vector decomposition technique for the normal and tangential directions is carefully considered in implementing the hypersingular equation in mathematical essence although we transform it to summability to divergent series. The five advantages, well-posed linear algebraic system, principal value free, elimination of boundary-layer effect, exponential convergence, and mesh free, are achieved. Several examples involving infinite, half-plane, and bounded domains with circular boundaries are given to demonstrate the validity of the proposed method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]

    Bi-criteria optimal control of redundant robot manipulators using LVI-based primal-dual neural network

    OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2010
    Binghuang Cai
    Abstract In this paper, a bi-criteria weighting scheme is proposed for the optimal motion control of redundant robot manipulators. To diminish the discontinuity phenomenon of pure infinity-norm velocity minimization (INVM) scheme, the proposed bi-criteria redundancy-resolution scheme combines the minimum kinetic energy scheme and the INVM scheme via a weighting factor. Joint physical limits such as joint limits and joint-velocity limits could also be incorporated simultaneously into the scheme formulation. The optimal kinematic control scheme can be reformulated finally as a quadratic programming (QP) problem. As the real-time QP solver, a primal-dual neural network (PDNN) based on linear variational inequalities (LVI) is developed as well with a simple piecewise-linear structure and global exponential convergence to optimal solutions. Since the LVI-based PDNN is matrix-inversion free, it has higher computational efficiency in comparison with dual neural networks. Computer simulations performed based on the PUMA560 manipulator illustrate the validity and advantages of such a bi-criteria neural optimal motion-control scheme for redundant robots. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Sharp interface limit for invariant measures of a stochastic Allen-Cahn equation

    COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2010
    Hendrik Weber
    The invariant measure of a one-dimensional Allen-Cahn equation with an additive space-time white noise is studied. This measure is absolutely continuous with respect to a Brownian bridge with a density that can be interpreted as a potential energy term. We consider the sharp interface limit in this setup. In the right scaling this corresponds to a Gibbs-type measure on a growing interval with decreasing temperature. Our main result is that in the limit we still see exponential convergence towards a curve of minimizers of the energy if the interval does not grow too fast. In the original scaling, the measure is concentrated on configurations with precisely one jump. © 2010 Wiley Periodicals, Inc. [source]