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We consider the problem of estimating the mean of a symmetric log-concave distribution under the constraint that only a single bit per sample from this distribution is available to the estimator. We study the mean squared error as a function of the sample size (and hence the number of bits). We consider three settings: first, a centralized setting, where an encoder may release $n$ bits given a sample of size $n$ , and for which there is no asymptotic penalty for quantization; second, an adaptive setting in which each bit is a function of the current observation and previously recorded bits, where we show that the optimal relative efficiency compared to the sample mean is precisely the efficiency of the median; lastly, we show that in a distributed setting where each bit is only a function of a local sample, no estimator can achieve optimal efficiency uniformly over the parameter space. We additionally complement our results in the adaptive setting by showing that one round of adaptivity is sufficient to achieve optimal mean-square error. [ABSTRACT FROM AUTHOR]

The accuracy of the adaptive cross approximation (ACA) algorithm, a popular method for the compression of low-rank matrix blocks in method of moment computations, is sometimes seriously compromised by unpredictable errors in the convergence criterion. This article proposes an alternative criterion based on global sampling of the error in the elements of the ACA compressed matrix. The sampling error depends not only on the size of the sample but also on the population distribution of the error, which makes it difficult to control the error independently of the underlying problem. However, as argued and demonstrated in this article, the distribution of the error converges to the same unique probability distribution function for all low-rank matrices. Complementing the sampling criterion with a simple mechanism to detect this convergence, we arrive at a criterion that controls the error irrespective of the underlying problem. As a practical example, the RCS of a moderate size metallic ogive is computed to illustrate the merits of the proposed criterion. The proposed algorithm may also be useful in other methods that approximate low-rank matrices by interpolation of a reduced set of its elements. [ABSTRACT FROM AUTHOR]

This paper addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized in space by the finite element method. Both methods yield numerical approximations such that the total error is split into stochastic and spatial contributions. We propose a particular implementation where the spatial error is controlled based on a Richardson extrapolation-based error indicator. The stochastic error, in turn, is efficiently reduced in the MLMC approach by distributing the samples on multiple grids. The method is applied to a toy problem with closed-form solution and to a permanent magnet synchronous machine with uncertainties. The uncertainties under consideration are related to the material properties in the stator and the magnets in the rotor. The examples show that the error indicator works reliably, the meshes used for the different levels do not have to be nested, and, most importantly, MLMC reduces the computational cost by at least one order of magnitude compared to standard Monte Carlo. [ABSTRACT FROM AUTHOR]

The control of automobile electronic throttle (AET) systems is a challenging task owing to multiple nonlinearities, i.e., transmission friction, gear backlash, limp-home spring set, and external load disturbance. In this paper, a practical tracking control scheme of an AET system is developed using a continuous fast nonsingular terminal sliding mode (CFNTSM) technique based on uncertainty observer. By using the prescribed CFNTSM surface and fast terminal sliding mode-based reaching element, the proposed control implementation guarantees the fast error convergence characteristic and high tracking accuracy under parameter uncertainties and perturbations. Furthermore, due to the adoption of the finite-time exact observer (FEO) for the lumped uncertainty estimation in the controller, the ease of the selection of the control gains is well-achieved since they only depend on the uncertainty estimation error. The closed-loop stability and finite-time convergence are presented based on the Lyapunov stability theory. Experimental verifications are conducted to validate the remarkable performance of the proposed control, in terms of the step and sinusoidal tracking as well as anti-disturbance ability. [ABSTRACT FROM PUBLISHER]

In this paper, an iterative method is proposed to solve the nonlinear Bitsadze–Samarskii boundary value problems with multi-point boundary conditions. The algorithm is based on the reproducing kernel Hilbert space method. We use an iterative scheme to overcome the nonlinearity of the problem. The convergence and error estimate of the iterative scheme are established. The reproducing kernel Hilbert space method is used to generate an approximation of the linearized problem. In fact, the reproducing kernel Hilbert space method is combined with an iterative scheme to approximate the solution and an error estimate of the approximate solution is derived. In order to show the efficiency and versatility of the proposed method, some numerical results are reported. The comparison of numerical results with the analytical solution and the best results reported in the literature confirms the good accuracy and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

The meshless element-free Galerkin method is developed for numerical analysis of hyperbolic initial-boundary value problems. In this method, only scattered nodes are required in the domain. Computational formulae of the method are analyzed in detail. Error estimates and convergence are also derived theoretically and verified numerically. Numerical examples validate the performance and efficiency of the method. [ABSTRACT FROM AUTHOR]

Switched systems theory is used to analyze the stability of image-based observers for three-dimensional localization of objects in a scene in the presence of intermittent measurements due to occlusions, feature tracking losses, or a limited camera field of view, for example. Generally, observers or filters that are exponentially stable under persistent measurement availability may have unbounded error growth under intermittent measurement loss, even while providing seemingly accurate state estimates. By constructing a framework that utilizes a state predictor during periods when measurements are not available, a class of image-based observers is shown to be exponentially convergent in the presence of intermittent measurements if an average dwell time, and a total unmeasurability time, condition is satisfied. The conditions are developed in a general form, applicable to any observer that is exponentially convergent assuming persistent visibility, and utilizes object motion knowledge to reduce the amount of time measurements must be available to maintain convergence guarantees. Based on the stability results, simulations are provided to show improved performance compared to a zero-order hold approach, where state estimates are held constant when measurements are not available. Experimental results are also included to verify the theoretical results, to demonstrate applicability of the developed observer and predictor design, and to compare against a typical approach using an extended Kalman filter. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel method of estimating the Fourier transform (FT) of deterministic, continuous-time signals, from a finite number N of their samples taken from a fixed-length observation window. It uses alias-free hybrid-stratified sampling to probe the processed signal at a mixture of deterministic and random time instants. The FT estimator, specifically designed to work with this sampling scheme, is unbiased, consistent and fast converging. It is shown that if the processed signal has continuous third derivative, then the estimator’s rate of uniform convergence in mean square is N^-5. Therefore, in terms of frequency-independent upper bounds on the FT estimation error, the proposed approach significantly outperforms existing estimators that utilize alias-free sampling, such as total random, stratified sampling, and antithetical stratified whose rate of uniform convergence is N^-1. It is proven here that N^-1 is a guaranteed minimum rate for all stratified-sampling-based estimators satisfying four weak conditions formulated in this paper. Owing to the alias-free nature of the sampling scheme, no constraints are imposed on the spectral support of the processed signal or the frequency ranges for which the Fourier Transform is estimated. [ABSTRACT FROM AUTHOR]