In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.
Ball and Plate (B&P) system is a benchmark system in the control engineering field that has been used to verify many control methods. In this paper the design of a sliding mode . controller has been investigated and verified in real-time via implementation on a real ball and plate system hardware. The mathematical model has been derived and the necessary parameters have been measured. The sliding mode controller has been designed based on the obtained mathematical model. The resulting controller has been implemented using the Arduino Mega 2560 and a ball and plate system built completely from scratch. The Arduino has been programmed by the Arduino support target for Simulink. Three test signals has been used for verification purposes
... Show MoreCensure in poetry is a pattern of poetic construction, in which the poet evokes a voice other than his own voice or creates out of his own self another self and engages with him in dialogue in the traditional artistic style whose origin remains unknown. Example of the same may be found in the classical Arabic poets’ stopping over the ruins, crying over separation and departure and speaking with stones and andirons; all in the traditional technical mould. Censure confronting the poet usually emanates from the women as blaming, censure and cursing is closer to woman’s hearts than to the man’ hearts. Censure revolves around some social issues, such as the habit of over drinking wine and extravagant generosity taking risks, traveling,
... Show MoreContinuous functions are novel concepts in topology. Many topologists contributed to the theory of continuous functions in topology. The present authors continued the study on continuous functions by utilizing the concept of gpα-closed sets in topology and introduced the concepts of weakly, subweakly and almost continuous functions. Further, the properties of these functions are established.
This paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.
In this paper, we present some numerical methods for solving systems of linear FredholmVolterra integral equations of the second kind. These methods namely are the Repeated Trapezoidal Method (RTM) and the Repeated Simpson's 1/3 Method (RSM). Also some numerical examples are presented to show the efficiency and the accuracy of the presented work.
Partial shading is one of the problems that affects the power production and the efficiency of photovoltaic module. A series of experimental work have been done of partial shading of monocrystalline PV module; 50W, Isc: 3.1A, Voc: 22V with 36 cells in series is achieved. Non-linear power output responses of the module are observed by applying various cases of partial shading (vertical and horizontal shading of solar cells in the module). Shading a single cell (corner cell) has the greatest impact on output energy. Horizontal shading or vertical shading reduced the power from 41W to 18W at constant solar radiation 1000W/m2 and steady state condition. Vertical blocking a column
... Show MoreMany numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.
The goal (purpose) from using development technology that require mathematical procedure related with high Quality & sufficiency of solving complex problem called Dynamic Programming with in recursive method (forward & backward) through finding series of associated decisions for reliability function of Pareto distribution estimator by using two approach Maximum likelihood & moment .to conclude optimal policy