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The Continuous Classical Boundary Optimal Control of Triple Nonlinear Elliptic Partial Differential Equations with State Constraints

    Our aim in this work is to study the classical continuous boundary control vector  problem for triple nonlinear partial differential equations of elliptic type involving a Neumann boundary control. At first, we prove that the triple nonlinear partial differential equations of elliptic type with a given classical continuous boundary control vector have a unique "state" solution vector,  by using the Minty-Browder Theorem. In addition, we prove the existence of a classical continuous boundary optimal control vector ruled by the triple nonlinear partial differential equations of elliptic type with equality and inequality constraints. We study the existence of the unique solution for the triple adjoint equations related with the triple state equations.

The Fréchet derivative is obtained. Finally we prove the theorems of both the necessary and sufficient conditions for optimality of the triple nonlinear partial differential equations of elliptic type through the Kuhn-Tucker-Lagrange's Multipliers theorem with equality and inequality constraints.

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Publication Date
Fri Mar 31 2017
Journal Name
Al-khwarizmi Engineering Journal
Design of Nonlinear PID Neural Controller for the Speed Control of a Permanent Magnet DC Motor Model based on Optimization Algorithm

In this paper, the speed control of the real DC motor is experimentally investigated using nonlinear PID neural network controller. As a simple and fast tuning algorithm, two optimization techniques are used; trial and error method and particle swarm optimization PSO algorithm in order to tune the nonlinear PID neural controller's parameters and to find best speed response of the DC motor. To save time in the real system, a Matlab simulation package is used to carry out these algorithms to tune and find the best values of the nonlinear PID parameters. Then these parameters are used in the designed real time nonlinear PID controller system based on LabVIEW package. Simulation and experimental results are compared with each other and showe

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Publication Date
Sun Oct 01 2023
Journal Name
Ijid Regions
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Publication Date
Sat Sep 30 2017
Journal Name
Al-khwarizmi Engineering Journal
A Cognitive Hybrid Tuning Control Algorithm Design for Nonlinear Path-Tracking Controller for Wheeled Mobile Robot

Abstract

This research presents a on-line cognitive tuning control algorithm for the nonlinear controller of path-tracking for dynamic wheeled mobile robot to stabilize and follow a continuous reference path with minimum tracking pose error. The goal of the proposed structure of a hybrid (Bees-PSO) algorithm is to find and tune the values of the control gains of the nonlinear (neural and back-stepping method) controllers as a simple on-line with fast tuning techniques in order to obtain the best torques actions of the wheels for the cart mobile robot from the proposed two controllers. Simulation results (Matlab Package 2012a) show that the nonlinear neural controller with hybrid Bees-PSO cognitive algorithm is m

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Publication Date
Sun Sep 06 2009
Journal Name
Baghdad Science Journal
Extension of the Chebyshev Method of Quassi-Linear Parabolic P.D.E.S With Mixed Boundary Conditions

The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

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Publication Date
Wed Nov 21 2018
Journal Name
International Journal Of Control, Automation And Systems
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Publication Date
Fri Feb 10 2023
Journal Name
Journal Of Applied Mathematics
The Dynamics of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat

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Publication Date
Tue Jun 01 2021
Journal Name
Baghdad Science Journal
Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

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Publication Date
Wed Aug 30 2023
Journal Name
Iraqi Journal Of Science
IoT-Key Agreement Protocol Based on The Lowest Work-Load Versions of The Elliptic Curve Diffie-Hellman

     A key agreement protocol (KAP) is a fundamental block in any cryptosystem since it ensures secure communication between two parties. Furthermore, KAP should include advanced features in limited-resource environments such as IoT, in which this protocol must be lightweight and efficient in consuming resources. Despite the Elliptic Curve Diffie-Hellman (ECDH) algorithm having often been considered efficient in providing an acceptable security degree with less resource consumption, it has suffered from weakness against Man-In-The-Middle Attacks (MITMA). This paper presents two versions of the Variant Elliptic Curve Diffie-Hellman (VECDH) algorithms as a key agreement protocol. The security analysis indicates that the proposed algori

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Publication Date
Mon Oct 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Fuzzy Multi-Objective Capacitated Transportation Problem with Mixed Constraints using different forms of membership functions

In this research, the problem of multi- objective modal transport was formulated with mixed constraints to find the optimal solution. The foggy approach of the Multi-objective Transfer Model (MOTP) was applied. There are three objectives to reduce costs to the minimum cost of transportation, administrative cost and cost of the goods. The linear membership function, the Exponential membership function, and the Hyperbolic membership function. Where the proposed model was used in the General Company for the manufacture of grain to reduce the cost of transport to the minimum and to find the best plan to transfer the product according to the restrictions imposed on the model.

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Publication Date
Thu Apr 18 2019
Journal Name
Al-kindy College Medical Journal
The state of Vitamin D in Iraqi Patients With Parkinson Disease

Background: A role for vitamin D deficiency in Parkinson disease (PD) has recently been suggested.

Objective:: To estimate the state of vitamin D in PD with an age-matched healthy control.

Type of the study: A case control study.

Method: The study randomly comparison of plasma 25-hydroxyvitamin D (25[OH] D) concentrations of collected samples in a clinical neurology department ward / Baghdad teaching hospital / Medical City and Parkinson disease movement disorder clinic. Participants were registered into the study from October 2015 to October 2016. We was study   serum vitamin D level in 40 consecutive patients with

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