A Multiple Power Reachable Sliding Mode Control Approach for Guidance of Miniature Laser Beam Riding Steered Munition

For a two-stage launch miniature shoulder munition steered with a laser beam riding system, the laser beam points to the target with a limited field radius and approximate straight-line spatial path; thus, the munition could not fly into the laser information field after the powered flight. The miniature munition dynamics are established firstly; then, an adaptive multiple power reachable sliding mode controller is presented and adopted to constrain both the trajectory inclination and pitch angle, which makes the munition enter the field and fly under control in the field with desired attitude angles, respectively. Considering the constraints of the incidence angle and the radius of the laser information field, an arctangent function curve is selected as the expected trajectory, and an adaptive multiple power reachable integral sliding mode guidance law is detailed, which makes the munition trajectory approach and converges to the expected curve fastly with limited acceleration. Therefore, the miniature munition flight trajectory is planned and optimized. Convergence and stability are analyzed based on the Lyapunov method. The numerical simulation against the stationary target is performed to fully demonstrate the efficacy of the proposed method.

DEVELOPMENT OF BIOMETRIC IDENTIFICATION METHODS BASED ON NEW FILTRATION METHODS

The article is devoted to the development of biometric identification methods based on new filtration methods. Biometric identification systems need constant improvement, because they often work slowly and give the wrong result. To increase the reliability of biometric image recognition, the method is formed, which is formed from the stages: segmentation, normalization, local orientation estimation, local estimation, spine frequency estimation, Gabor filter implementation, binarization, thinning. A new filtering method is proposed, which is based on a new type of function – Ateb-functions, which are used next to the Gabor filter. The local orientation can be calculated from local gradients using the arctangent function. The normalization process is performed to evenly redistribute the values ​​of image intensity. When segmenting, the foreground areas in the image are separated from the background areas. A new method of wavelet conversion of biometric image filtering based on Ateb-Gabor has been developed. The Gabor filter is used for linear filtering and improves the quality of the converted image. Symmetry and wavelet transform operations are also used to reduce the number of required multiplication and addition operations. The method is based on the well-known Gabor filter and allows you to rearrange the image with clearer contours. Therefore, this method is applicable to biometric images, where the creation of clear contours is particularly relevant. When Gabor filtering, the image is reconstructed by multiplying the harmonic function by the Gaussian function. Ateb functions are a generalization of elementary trigonometry, and, accordingly, have greater functionality. Ateb-Gabor filtering allows you to change the intensity of the whole image, as well as the intensity in certain ranges, and thus make certain areas of the image more contrasting. Filtering with Ateb functions allows you to change the image from two rational parameters. This allows you to more flexibly manage filtering and choose the best options. When you perform a thinning, the foreground pixels are erased until there is one pixel wide. A standard thinning algorithm is used, or the thinning developed by the authors in other studies. This filtering will provide more accurate characteristics, as it allows you to get more sloping shapes and allows you to organize a wider range of curves. Numerous experimental studies indicate the effectiveness of the proposed method.

Modeling of multistage nonlinear Dual Mass Flywheel torsional damper based on smoothing function fitting

The smoothing function is used to solve the problem of low simulation efficiency of multi-stage stiffness Dual Mass Flywheel (DMF) model, and the influence of different smoothing functions and fitting factor β on the fitting effect is studied. Firstly, based on the analysis of the working principle of multi-stage stiffness DMF, a mathematical model of DMF considering multi-stage stiffness and damping nonlinearity is established, and the accuracy of the model is verified by bench test. Then, tanh function, arctangent function, and sigmoid function are used to smooth the segment points in the DMF model, which solves the problem of inefficiency and not easy to converge in simulation. Finally, a 3-DOF model of the transmission system with DMF is established to simulate and analyze the smooth effect of the smoothing function and the performance difference between different smoothing functions. The results show that the smoothing function can effectively improve the stability of the simulation model. By comparing the three smoothing functions, it can be seen that the sigmoid function has the most obvious effect, which can shorten the simulation time by 52%.

Speed and accuracy improvements in standard algorithm for prismatic gravitational field

SUMMARY By utilizing the addition theorems of the arctangent function and the logarithm, we developed a new expression of Bessel’s exact formula to compute the prismatic gravitational field using the triple difference of certain analytic functions. The use of the new expression is fast since the number of transcendental functions required is significantly reduced. The numerical experiments show that, in computing the gravitational potential, the gravity vector, and the gravity gradient tensor of a uniform rectangular parallelepiped, the new method runs 2.3, 2.3 and 3.7 times faster than Bessel’s method, respectively. Also, the new method achieves a slight increase in the computing precision. Therefore, the new method can be used in place of Bessel’s method in any situation. The same approach is applicable to the geomagnetic field computation.

Refined Estimates and Generalizations of Inequalities Related to the Arctangent Function and Shafer’s Inequality

We give some sharper refinements and generalizations of inequalities related to Shafer’s inequality for the arctangent function, stated in Theorems 1, 2, and 4 in Mortici and Srivastava, 2014, by C. Mortici and H.M. Srivastava.