Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
2
1
2017
04
01
A Computational Method for Solving Optimal Control Problems and Their Applications
1
13
EN
Zahra
Rafiei
Department of Mathematics, Yazd University, Yazd, Iran
z.rafiei@stu.yazd.ac.ir
Behzad
Kafash
Assistant Professor, Faculty of Engineering, Ardakan University, Ardakan, Iran
zrrafiei87@gmail.com
Seyyed Mehdi
Karbassi
Department of Mathematics, Yazd University, Yazd, Iran
smkarbassi@yazd.ac.ir
In order to obtain a solution to an optimal control problem, a numerical technique based on state-control parameterization method is presented. This method can be facilitated by the computation of performance index and state equation via approximating the control and state variable as a function of time. Several numerical examples are presented to confirm the analytical findings and illustrate the efficiency of the proposed method.
Optimal control,State-control parameterization,Basis polynomials
https://mathco.journals.pnu.ac.ir/article_4819.html
https://mathco.journals.pnu.ac.ir/article_4819_1ccc5fa900244ba6d3e16e1726ac7d13.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
2
1
2017
04
01
A New Approach for Solving Grey Assignment Problems
15
28
EN
Hadi
Nasseri
Department of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
nasseri@umz.ac.ir
Davood
Darvishi Salokolaei
0000-0001-5039-2469
Department of Mathematics, Payame Noor University, Tehran, Iran
darvishidavood@yahoo.com
Allahbakhsh
Yazdani
0000-0002-3352-5829
Department of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
yazdani@umz.ac.ir
Linear assignment problem is one of the most important practical models in the literature of linear programming problems. Input data in the cost matrix of the linear assignment problem are not always crisp and sometimes in the practical situations is formulated by the grey systems theory approach. In this way, some researchers have used a whitening technique to solve the grey assignment problem. Since the whitening technique only provides a crisp equivalent model and does not reflect the evolutionary characteristics of a grey set, it cannot keep the uncertainty properties in an interval involving the optimal solution. Based on these shortcomings, in this paper a new direct approach is introduced to solve linear assignment problem in grey environments. For preparing the mentioned method, some theoretical results are given to support the methodology. Finally, a numerical example will be solved to test the validity of the proposed method. Based on the suggested methodology, we emphasize that the same approach can be used whenever any linear programming model is formulated in grey environments.
Assignment problem,Grey system theory,Grey number,Uncertainty,Whitening technique
https://mathco.journals.pnu.ac.ir/article_4820.html
https://mathco.journals.pnu.ac.ir/article_4820_ce1ebfe26971053cf5e43e7837555a8f.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
2
1
2017
04
01
Optimization of Energy Consumption in Image Transmission in Wireless Sensor Networks (WSNs) using a Hybrid Method
29
41
EN
Abbas Ali
Rezaee
Assistant Professor, Department of Computer Engineering and Information Technology, Payame Noor University,Tehran, IRAN
abbasrezae@gmail.com
Farnoosh
Zareian
Department of Computer Engineering and Information Technology, Payame Noor University, International Center of Assaluyeh, Assaluyeh, Iran
f.zareiyan68@gmail.com
In wireless sensor networks (WSNs), sensor nodes have limited resources with regard to computation, storage, communication bandwidth, and the most important of all, energy supply. In addition, in many applications of sensor networks, we need to send images to a sink node. Therefore, we have to use methods for sending images in which the number and volume of packets are optimized to save energy. Data compression is one of the optimization methods in energy consumption. In this paper, an effective compression algorithm is proposed to reduces computational and energy consumption and eventually, increases the overall network lifetime. Here in, we use a combination of three DCT, DWT and SWT wavelet transforms to achieve our goals. Simulation results show that the proposed algorithm achieves its goals with regard to data compression and reduction of energy consumption, and improves the network lifetime.
Wireless sensor networks,Energy consumption,Image compression,Discrete wavelet transform,Discrete cosine transforms,Static wavelet transforms
https://mathco.journals.pnu.ac.ir/article_4821.html
https://mathco.journals.pnu.ac.ir/article_4821_1a49a63a1dc9ac9b365b1fbcfa30eb2b.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
2
1
2017
04
01
Solving Second Kind Volterra-Fredholm Integral Equations by Using Triangular Functions (TF) and Dynamical Systems
43
63
EN
Azhdar
Soleymanpour Bakefayat
Department of Mathematics, Farhangian University, Tehran, Iran
asad87000@yahoo.com
Sima
Karamseraji
Department of Mathematics, Karaj Branch, Islamic Azad University, Alborz, Iran
rimakool2002@yahoo.com
The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp). The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system. In this article, the obtained nonlinear system has been solved as a dynamical system. The solution of the obtained nonlinear system by the dynamical system through the Newton numerical method has got a particular priority, in that, in this method, the number of the unknowns could be more than the number of equations. Besides, the point of departure of the system could be an infeasible point. It has been proved that the obtained dynamical system is stable, and the response of this system can be achieved by using of the fourth order Runge-Kutta. The results of this method is comparable with the similar numerical methods; in most of the cases, the obtained results by the presented method are more efficient than those obtained by other numerical methods. The efficiency of the new method will be investigated through examples.
Second kind Fredholm-Volterra integral equations,Nonlinear systems,Dynamical systems,Triangular functions,Block-pulse functions
https://mathco.journals.pnu.ac.ir/article_4822.html
https://mathco.journals.pnu.ac.ir/article_4822_e8a61ae5105640197527a9613b607267.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
2
1
2017
04
01
A New Approach for Approximating Solution of Continuous Semi-Infinite Linear Programming
65
76
EN
Alireza
Fakharzadeh Jahromi
Department of Mathematics, Shiraz University of Technology, Shiraz,
Iran
a_fakharzadeh@sutech.ac.ir
Zahra
Alamdar Ghahferokhi
Department of Mathematics, Shiraz University of Technology, Shiraz,
Iran
zhalamdar@gmail.com
This paper describes a new optimization method for solving continuous semi-infinite linear problems. With regard to the dual properties, the problem is presented as a measure theoretical optimization problem, in which the existence of the solution is guaranteed. Then, on the basis of the atomic measure properties, a computation method was presented for obtaining the near optimal solution by means of famous and simple simplex method. Some numerical results are reported to indicate the efficiency of the new method.
Atomic measure,Linear programming,Radon measure,Semi-infinite linear programming,Weak* topology
https://mathco.journals.pnu.ac.ir/article_4823.html
https://mathco.journals.pnu.ac.ir/article_4823_0df3f50a369c00d38b6dee3a1034a1b5.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
2
1
2017
04
01
Numerical Solution of the Controlled Harmonic Oscillator by Homotopy Perturbation Method
77
91
EN
Seyed Mehdi
Mirhosseini-Alizamini
0000-0003-1433-3124
Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
seyedmehdi_mirhosseini@yahoo.com
The controlled harmonic oscillator with retarded damping, is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems. In this paper, to solve this problem, we presented an analytical method. This approach is based on the homotopy perturbation method. The solution procedure becomes easier, simpler and more straightforward. In order to use the proposed method, a control design algorithm with low computational complexity is presented. Through the finite iterations of the proposed algorithm, a suboptimal control law is obtained for the problems. Finally, the obtained results have been compared with the exact solution of the controlled harmonic oscillator and variational iteration method, so that the high accuracy of the results is clear.
Suboptimal control,Harmonic oscillator,Damping,Homotopy perturbation method
https://mathco.journals.pnu.ac.ir/article_4824.html
https://mathco.journals.pnu.ac.ir/article_4824_48f723fa96ec161d4caddbf43991cc71.pdf