Advances on the extended stochastic rayleigh quotient estimation theory

A new extended stochastic Rayleigh quotient estimation theory is developed for the identification of the unknown feedback matrix and nonlinear function parameters of a proposed multivariable plant. Systems tractable to this approach encompass a wide class of nonlinear closed-loop time-variant control models that are observed at two localities in a statistically-known white Gaussian noisy environment. Phases of the estimation problem via a partitioning frame technique are given that yield pragmatical computable solutions. An optimal modified-predictor—corrector maximum-likelihood scheme is delineated for solving the state estimation problem, and its invariance to a priori statistics is investigated. In addition, this article presents the analysis of extended stochastic Rayleigh quotient algorithms, extended SRQA's, for the evaluation of the unknown parameters. Nonlinear programming formulations are treated for the algorithms' commencement. Moreover, a noncyclic adaptive computational procedure is depicted to ensure the pointwise convergence of the extended SRQA's in the mean-square sense. Finally, applicability of the devised theory to a nonlinear third-order system is demonstrated as well as a comparison between different suggested methods

RIDGE LEAST ABSOLUTE DEVIATION PERFORMANCE IN ADDRESSING MULTICOLLINEARITY AND DIFFERENT LEVELS OF OUTLIER SIMULTANEOUSLY

If there is multicollinearity and outliers in the data, the inference about parameter estimation in the LS method will deviate due to the inefficiency of this method in estimating. To overcome these two problems simultaneously, it can be done using robust regression, one of which is ridge least absolute deviation method. This study aims to evaluate the performance of the ridge least absolute deviation method in surmounting multicollinearity in divers sample sizes and percentage of outliers using simulation data. The Monte Carlo study was designed in a multiple regression model with multicollinearity (ρ=0.99) between variables  and  and outliers 10%, 20%, 30% on response variables with different sample sizes (n = 25, 50,75,100,200; =0, and β=1 otherwise). The existence of multicollinearity in the data is done by calculating the correlation value between the independent variables and the VIF value. Outlier detection is done by using boxplot. Parameter estimation was carried out using the RLAD and LS methods. Furthermore, a comparison of the MSE values of the two methods is carried out to see which method is better in overcoming multicollinearity and outliers. The results showed that RLAD had a lower MSE than LS. This signifies that RLAD is more precise in estimating the regression coefficients for each sample size and various outlier levels studied

Penyelesaian Sistem Persamaan Fully Fuzzy Non Linear Menggunakan Metode Newton Raphson Ganda

Terdapat banyak permasalahan dunia nyata yang diupayakan penyelesaiannya menggunakan sistem persamaan yang melibatkan himpunan bilangan fuzzy. Sistem persamaan fuzzy non linear dikembangkan menjadi sistem persamaan fully fuzzy nonlinear dengan mengimplementasikan operasi aritmatika bilangan fuzzy. Artikel ini bertujuan mendeskripsikan penyelesaian sistem persamaan fully fuzzy non linear yang melibatkan bilangan segitiga fuzzy dengan menggunakan alat bantu komputasi (algoritma dan pemrograman) dengan melibatkan metode Newton Raphson Ganda. Teknis mendapatkan solusi menggunakan metode ini dapat dicapai dengan terlebih dahulu melakukan transformasi sistem persamaan fuzzy ke dalam sistem persamaan nonlinear dengan bilangan tegas menggunakan operasi aritmatika bilangan fuzzy segitiga. Komputasi penentuan solusi didasari pada sebuah algoritma yang implementasinya ke dalam program Matlab. Algoritma dan program Matlab yang dibuat memperlihatkan bahwa Newton Raphson Ganda dapat menyelesaikan sistem persamaan fully fuzzy non linear dengan efesien dalam waktu dan akurat dalam nilai hampiran solusi

Design of gain schedule fractional PID control for nonlinear thrust vector control missile with uncertainty

The purpose of this paper is to control the trajectory of the nonlinear missile model in the pitch channel by using Fractional PID controller (FPID) and Gain Schedule Fractional PID controller (GSFPID). FPID and GSFPID with nonlinear missile model are designed where their parameters are tuned by Simulink design optimization in the Matlab toolbox. This optimization method gives the optimal parameters that achieve the best tracking with step unit reference signal. The GSFPID controller compensates the restrictions that represent physical limits of actuators in the pitch channel. The GSFPID with nonlinear missile model is designed in two phases. The first phase is the boost phase where the thrust force is maximized and the second phase is sustain phase where the thrust force is minimized. The equations of motion for nonlinear missile model with FPID and GSFPID are modelled mathematically in the Matlab-Simulink environment. The results of FPID and GSFPID controllers with the nonlinear missile model are presented and compared. The wind effect and the dynamic uncertainties effects are researched and the results are compared. The closed-loop nonlinear system is linearized by the Simulink linear analysis tool at critical operating point t = 5.8 sec and the stability is studied

PEMODELAN MATEMATIKA LAJU ALIRAN PANAS PADA WAJAN PEMBUATAN ARANG AKTIF-13 DENGAN MENGGUNAKAN METODE BEDA HINGGA (FINITE DIFFERENCE METHOD)

In this paper we propose the theory of finite difference methode for calculating heat transfer on rectangular tin pan alloy which the  center temperature is 7000c and the ambien temperature is 300 c. The aim in this paper we used this method for calculating of heat transfer on the pan in order to process of making activated charcoal especially called “arang aktif-13”. We design a furnace which is the heat resources in the center only then choosing 9 points rectangularly on the plate pan that it will be calculated the value of temperature and the velocity of temperature on these points. By assumption the temperature at the center of the pan on the furnice is consistence or stable, then we do the process of defried of row material coconut shell until cooked as activated charcoal. We consider choosing 9 points in order tobe caculated as manually easiely and therefore can be comparing with using software lindo, and also for more points grather than 9 we suggested using masine more efficient. The spreading of the heat on the plate pan when the moment achieve the condition of the temperature araund the pan stable, then it can be animated by using software matlab. By doing depried of row material, that process will need 13 minutes to become activated charcoal

Rotatum of Light

Vortices are ubiquitous in nature and can be observed in fluids, condensed matter, and even in the formation of galaxies. Light, too, can evolve like a vortex. Optical vortices are exploited in light-matter interaction, free-space communications, and imaging. Here, we introduce optical rotatum; a new degree-of-freedom of light in which an optical vortex experiences a quadratic chirp in its orbital angular momentum along the optical path. We show that such an adiabatic deformation of topology is associated with the accumulation of a Berry phase factor which in turn perturbs the propagation constant (spatial frequency) of the beam. Remarkably, the spatial structure of optical rotatum follows a logarithmic spiral; a signature that is commonly seen in the pattern formation of seashells and galaxies. Our work expands previous literature on structured light, offers new modalities for light-matter interaction, communications, and sensing, and hints to analogous effects in condensed matter physics and Bose-Einstein condensates.Comment: 24 Pages, 4 Main Figures, 2 Extended Figure