Haar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems
Saeed
Nezhadhosein
Department of Applied Mathematics, Payame Noor University, Tehran, 193953697, Iran
author
text
article
2017
eng
In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, Haar wavelets are applied for converting the TBVP, as a system of differential equations, in to a system of matrix algebraic equations, as Haar matrix equations using Kronecker product. Then the error analysis of the proposed method is presented. Some numerical examples are given to demonstrate the efficiency of the method. The solutions converge as the number of approximate terms increase.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
2
v.
2
no.
2017
1
14
https://mathco.journals.pnu.ac.ir/article_5726_39c990da2be15864978cbf6bbbeb5534.pdf
Application of Grey System Theory in Rainfall Estimation
Davood
Darvishi Salookolaei
Assistant Professor, Department of Mathematics, Payame Noor University, Tehran, Iran.
author
Sifeng
Liu
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China
author
Parvin
Babaei
Master of Science, Department of Mathematics, Payame Noor University, Tehran, Iran.
author
text
article
2017
eng
Considering the fact that Iran is situated in an arid and semi-arid region, rainfall prediction for the management of water resources is very important and necessary. Researchers have proposed various prediction methods that have been utilized in such areas as water and meteorology, especially water resources management. The present study aimed at predicting rainfall amounts using Grey Prediction Method. It is a novel approach in confrontation with uncertainties in the aquiferous region of Babolrud to serve for the water resources management purposes. Therefore, expressing the concepts of Grey Prediction Methods using the collected data, at a 12-year timeframe of 2006 and 2017, rainfall prediction in 2018 and 2022 were also implemented with three methods GM(1,1), DGM(2,1) and Verhulest models. According to the calculated error and the predictive power, GM(1,1) method is better than other models and was placed within the set of good predictions. Also, we predict that in 2027, there might be a drought. According to the small samples and calculations required in this approach, the method is suggested for rainfall prediction in inexact environments. The authors can use fuzzy grey systems to predict the amount of rainfall in uncertaint environments.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
2
v.
2
no.
2017
15
32
https://mathco.journals.pnu.ac.ir/article_5727_17c516939caa1fdd65c38ca36d074cf4.pdf
Two-Level Optimization Problems with Infinite Number of Convex Lower Level Constraints
Nader
Kanzi
Department of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, Iran
author
text
article
2017
eng
This paper proposes a new form of optimization problem which is a two-level programming problem with infinitely many lower level constraints. Firstly, we consider some lower level constraint qualifications (CQs) for this problem. Then, under these CQs, we derive formula for estimating the subdifferential of its valued function. Finally, we present some necessary optimality conditions as Fritz-John type for the problem.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
2
v.
2
no.
2017
33
44
https://mathco.journals.pnu.ac.ir/article_5731_e315ece4d1dc99cfd4e6be1448e73889.pdf
Global Asymptotic and Exponential Stability of Tri-Cell Networks with Different Time Delays
Zohreh
Dadi
Department of Mathematics, Faculty of Basic Sciences, University of
Bojnord, P.O. Box 1339, Bojnord 94531, Iran
author
Farzaneh
Ravanbakhsh
Department of Mathematics, Faculty of Basic Sciences, University of
Bojnord, P.O. Box 1339, Bojnord 94531, Iran
author
text
article
2017
eng
In this paper, a bidirectional ring network with three cells and different time delays is presented. To propose this model which is a good extension of three-unit neural networks, coupled cell network theory and neural network theory are applied. In this model, every cell has self-connections without delay but different time delays are assumed in other connections. A suitable Lyapunov function is presented for this model which helps to get sufficient conditions to guarantee asymptotic and exponential stability of the model. Also, these conditions are independent of time delays. Finally, analytical results are confirmed by numerical examples which are stated.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
2
v.
2
no.
2017
45
60
https://mathco.journals.pnu.ac.ir/article_5728_d7d8ad7196d54741fba48dee2dc364e3.pdf
Optimal Shape Design for a Cooling Pin Fin Connection Profil
Seyed Hamed
Hashemi Mehne
Assistant Professor of Aerospace Research Institute, Tehran, 14665-834, Iran.
author
Khodayar
Javadi
Department of Aerospace Engineering, Sharif University of Technology
author
text
article
2017
eng
A shape optimization problem of cooling fins for computer parts and integrated circuits is modeled and solved in this paper. The main purpose is to determine the shape of a two-dimensional pin fin, which leads to the maximum amount of removed heat. To do this, the shape optimization problem is defined as maximizing the norm of the Nusselt number distribution at the boundary of the pin fin's connection profile. The governing differential equations are solved in solid and fluid phases separately. In order to formulate the optimization problem with finite dimensions, the shapes of the profiles are parameterized with cubic polynomials. Due to the lack of an explicit relation between the objective function and the geometric parameters, an approximate modeling method is used for the optimization process. The proposed method starts with three initial points. Then, the governing differential equations are solved for each of the profiles related to the initial points. The new step in this iterative process involves calculations based on a polynomial interpolation within the resulting Nusselt number norms. A numerical example is given to show the implementation and accuracy of the method.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
2
v.
2
no.
2017
61
76
https://mathco.journals.pnu.ac.ir/article_5729_87708eb61cfd12941c88d00dc22a3b3c.pdf
Optimizing the Static and Dynamic Scheduling problem of Automated Guided Vehicles in Container Terminals
Hassan
Rashidi
Department of Mathematics and Computer Science, Allameh Tabataba’i University, Tehran, Iran,
author
text
article
2017
eng
The Minimum Cost Flow (MCF) problem is a well-known problem in the area of network optimisation. To tackle this problem, Network Simplex Algorithm (NSA) is the fastest solution method. NSA has three extensions, namely Network Simplex plus Algorithm (NSA+), Dynamic Network Simplex Algorithm (DNSA) and Dynamic Network Simplex plus Algorithm (DNSA+). The objectives of the research reported in this paper are to simulate and investigate the advantages and disadvantages of NSA compared with those of the three extensions in practical situations. To perform the evaluation, an application of these algorithms to scheduling problem of automated guided vehicles in container terminal is used. In the experiments, the number of iterations, CPU-time required to solve problems, overheads and complexity are considered.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
2
v.
2
no.
2017
77
101
https://mathco.journals.pnu.ac.ir/article_5730_fbbd6925e9091cab1b93c28d72353257.pdf