Discrete indirect adaptive sliding mode control for uncertain Hammerstein nonlinear systems

The robustness issue of uncertain nonlinear systems’ control has attracted the attention of numerous researchers. In this paper, we propose three techniques to deal with the uncertain Hammerstein nonlinear model. First, a discrete sliding mode control (SMC) is developed, which is based on converting the original nonlinear system into a linearized one in the vicinity of the operating region using Taylor series expansion. However, the presence of relatively high nonlinearities and parameter variations leads to the deterioration of the desired performances. In order to overcome these problems and to improve the performance of classical SMC, we propose two solutions. The first one is based on the synthesis of a discrete SMC, taking into account the presence of nonlinearity. The second solution is a new discrete adaptive SMC for input–output Hammerstein model. In order to show the effectiveness of the proposed controllers, a detailed robustness analysis is clearly developed. Simulation examples are reported at the end of the paper.

New full relativistic escape velocity and new Hubble related equation for the universe

The escape velocity derived from general relativity coincides with the Newtonian one. However, the Newtonian escape velocity can only be a good approximation when v ≪ c is sufficient to break free of the gravitational field of a massive body, as it ignores higher-order terms of the relativistic kinetic energy Taylor series expansion. Consequently, it does not work for a gravitational body with a radius at which v is close to c such as a black hole. To address this problem, we revisit the concept of relativistic mass, abandoned by Einstein, and derive what we call a full relativistic escape velocity. This approach leads to a new escape radius, where ve = c equal to a half of the Schwarzschild radius. Furthermore, we show that one can derive the Friedmann equation for a critical universe from the escape velocity formula from general relativity theory. We also derive a new equation for a flat universe based on our full relativistic escape velocity formula. Our alternative to the Friedmann formula predicts exactly twice the mass density in our (critical) universe as the Friedmann equation after it is calibrated to the observed cosmological redshift. Our full relativistic escape velocity formula also appears more consistent with the uniqueness of the Planck mass (particle) than the general relativity theory: whereas the general relativity theory predicts an escape velocity above c for the Planck mass at a radius equal to the Planck length, our model predicts an escape velocity c in this case.

On The Efficiency of Almost Unbiased Mean Imputation When Population Mean of Auxiliary Variable is UnknownOn The Efficiency of Almost Unbiased Mean Imputation When Population Mean of Auxiliary Variable is Unknown

Human-assisted surveys, such as medical and social science surveys, are frequently plagued by non-response or missing observations. Several authors have devised different imputation algorithms to account for missing observations during analyses. Nonetheless, several of these imputation schemes' estimators are based on known population meanof auxiliary variable. In this paper, a new class of almost unbiased imputation method that uses as an estimate of is suggested. Using the Taylor series expansion technique, the MSE of the class of estimators presented was derived up to first order approximation. Conditions were also specified for which the new estimators were more efficient than the other estimators studied in the study. The results of numerical examples through simulations revealed that the suggested class of estimators is more efficient.

Potential field data interpolation by Taylor series expansion

Data interpolation is critical in the analysis of geophysical data when some data is missing or inaccessible. We propose to interpolate irregular or missing potential field data using the relation between adjacent data points inspired by the Taylor series expansion (TSE). The TSE method first finds the derivatives of a given point near the query point using data from neighboring points, and then uses the Taylor series to obtain the value at the query point. The TSE method works by extracting local features represented as derivatives from the original data for interpolation in the area of data vacancy. Compared with other interpolation methods, the TSE provides a complete description of potential field data. Specifically, the remainder in TSE can measure local fitting errors and help obtain accurate results. Implementation of the TSE method involves two critical parameters – the order of the Taylor series and the number of neighbors used in the calculation of derivatives. We have found that the first parameter must be carefully chosen to balance between the accuracy and numerical stability when data contains noise. The second parameter can help us build an over-determined system for improved robustness against noise. Methods of selecting neighbors around the given point using an azimuthally uniform distribution or the nearest-distance principle are also presented. The proposed approach is first illustrated by a synthetic gravity dataset from a single survey line, then is generalized to the case over a survey grid. In both numerical experiments, the TSE method has demonstrated an improved interpolation accuracy in comparison with the minimum curvature method. Finally we apply the TSE method to a ground gravity dataset from the Abitibi Greenstone Belt, Canada, and an airborne gravity dataset from the Vinton Dome, Louisiana, USA.

Comparison Between Numerical Methods for Generalized Zakharov system

We present two numerical methods to get approximate solutions for generalized Zakharov system GZS. The first one is Legendre collocation method, which assumes an expansion in a series of Legendre polynomials , for the function and its derivatives occurring in the GZS, the expansion coefficients are then determined by reducing the problem to a system of algebraic equations. The second is differential transform method DTM , it is a transformation technique based on the Taylor series expansion. In this method, certain transformation rules are applied to transform the problem into a set of algebraic equations and the solution of these algebraic equations gives the desired solution of the problem.The obtained numerical solutions compared with corresponding analytical solutions.The results show that the proposed method has high accuracy for solving the GZS.

Quantum alchemy beyond singlets: Bonding in diatomic molecules with hydrogen

Bonding energies are key for the relative stability of molecules in chemical space. Therefore methods employed to search for relevant molecules in chemical space need to capture the bonding behavior for a wide range of molecules, including radicals. In this work, we investigate the ability of quantum alchemy to do so for exploring hypothetical chemical compounds, here diatomic molecules involving hydrogen with various electronic structures. We evaluate equilibrium bond lengths, ionization ener- gies, and electron affinities of these fundamental systems. We compare and contrast how well manual quantum alchemy calculations, i.e. quantum mechanical calculations in which the nuclear charge is altered, and quantum alchemy approximations using a Taylor series expansion can predict these molecular properties. We also investigate the extent of error cancellation of these approaches in terms of ionization energies and electron affinities when using thermodynamic cycles. Our results suggest that the accuracy of Taylor series expansions are greatly improved by error cancellation in thermodynamic cycles, and errors also appear to be generally system-dependent. Taken together, this work provides insights into how quantum alchemy predictions us- ing a Taylor series expansion may be applied to future studies of non-singlet systems as well as which challenges remain open for these cases.

Evaluating quantum alchemy of atoms with thermodynamic cycles: Beyond ground electronic states

Due to the sheer size of chemical and materials space, high throughput computational screening thereof will require the development of new computational methods that are accurate, efficient, and transferable. These methods need to be applicable to electron configurations beyond ground states. To this end, we have systematically studied the applicability of quantum alchemy predictions using a Taylor series expansion on quantum mechanics (QM) calculations for single atoms with different electronic structures arising from different net charges and electron spin multiplicities. We first compare QM method accuracy to experimental quantities including first and second ionization energies, electron affinities, and multiplet spin energy gaps for a baseline understanding of QM reference data. We then investigate the intrinsic accuracy of an approach we call "manual" quantum alchemy schemes compared to the same QM reference data, which employ QM calculations where the basis set of a different element is used for an atom as the limit case of quantum alchemy. We then discuss the reliability of quantum alchemy based on Taylor series approximations at different orders of truncation. Overall, we find that the errors from finite basis set treatments in quantum alchemy are significantly reduced when thermodynamic cycles are employed, which points out a route to improve quantum alchemy in explorations of chemical space. This work establishes important technical aspects that impact the accuracy of quantum alchemy predictions using a Taylor series and provides a foundation for further quantum alchemy studies.

Research on the Fast and Accurate Estimation Method of Sag Voltage

Sag voltage affects the quality of the grid voltage and the working conditions of the electrical equipment. In order to prevent effectively this problem, the authors investigated the estimation method of fast and accurate voltage and phase angle in the presence of sag voltage. The method proposed Least Error Squares (LES) were constructed on the basis of the least squares algorithm and Taylor series expansion. Compared with conventional Clark and Park methods, the LES approach has the following major advantages: faster detection time, reduced deviation of estimated voltage values at the time of failure; faster detection time, reduced deviation of estimated voltage values at the time of failure; being not affected by other fundamental components 50Hz, the DC components in the grid. The effectiveness of the method is verified by simulation model of a distribution grid in Vinh Phuc province by Matlab / SIMULINK software.