Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
3
1
2018
07
01
A Numerical Solution of Fractional Optimal Control Problems Using Spectral Method and Hybrid Functions
1
25
EN
seyed mehdy
shafiof
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran
sm.shafiof@gmail.com
Javad
Askari
Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
j-askari@cc.iut.ac.ir
Maryam
Shams Solary
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran
shamssolary@pnu.ac.ir
10.30473/coam.2019.46969.1119
In this paper, a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly. First, the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs). Then, the unknown functions are approximated by the hybrid functions, including Bernoulli polynomials and Block-pulse functions based on the spectral Ritz method. Also, two new methods are proposed for calculating the left Caputo fractional derivative and right Riemann-Liouville fractional derivative operators of the hybrid functions that are proportional to the Ritz method. The FOCP is converted into a system of the algebraic equations by applying the fractional derivative operators and collocation method, which determines the solution of the problem. Error estimates for the hybrid function approximation, fractional operators and, the proposed method are provided. Finally, the efficiency of the proposed method and its accuracy in obtaining optimal solutions are shown by some test problems.
Fractional optimal control,Hybrid functions,Bernoulli polynomials,Ritz method,Error bound
https://mathco.journals.pnu.ac.ir/article_6287.html
https://mathco.journals.pnu.ac.ir/article_6287_704ba4697435e956e25090929183272c.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
3
1
2018
07
01
A New Hybrid Conjugate Gradient Method Based on Eigenvalue Analysis for Unconstrained Optimization Problems
27
43
EN
Farzad
Rahpeymaii
Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran
rahpeyma_83@yahoo.com
majid
rostami
Young Researchers and Elite Club‎, ‎Hamedan Branch‎, ‎Islamic Azad University‎, ‎Hamedan‎, ‎Iran
majid403rostami@yahoo.com
10.30473/coam.2019.44564.1108
In this paper, two extended three-term conjugate gradient methods based on the Liu-Storey ({\tt LS})<br /> conjugate gradient method are presented to solve unconstrained optimization problems. A remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition independent of line search method, based on eigenvalue analysis. The global convergence of proposed algorithms is established under suitable conditions. Preliminary numerical results show that the proposed methods are efficient and robust to solve the unconstrained optimization problems.
Unconstrained optimization,Conjugate gradient methods,Eigenvalue analysis,Global convergence,Numerical comparisons
https://mathco.journals.pnu.ac.ir/article_6288.html
https://mathco.journals.pnu.ac.ir/article_6288_20121f1ee104cee144389de7993f9509.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
3
1
2018
07
01
Hybrid Time Delay Petri Nets as a Mathematical Novel Tool to Model Dynamic System with Current Sample Time
45
64
EN
Alireza
Ahangarani Farahani
Electrical and Computer Engineering Department, Semnan University, Semnan, Iran
a.ahangarani@semnan.ac.ir
Abbas
Dideban
Department of Electrical and Computer Engineering,Semnan university, Semnan, Iran
adideban@semnan.ac.ir
10.30473/coam.2019.41925.1090
The existing modeling methods using Petri Nets, have been successfully applied to model and analyze dynamic systems. However, these methods are not capable of modeling all dynamic systems such as systems with the current sample time signals, systems including various subsystems and multi-mode systems. This paper proposes Hybrid Time Delay Petri Nets (HTDPN) to solve the problem. In this approach, discrete and continuous Petri Nets are combined so that the continuous PNs part and the discrete PNs are responsible for past time samples and current sample time, respectively. To evaluate the performance of the proposed tool, it is employed to model a legless piezoelectric capsubot robot as a multi modes system and a $PID$ controller, in which the gains tuned by the Genetic Algorithm are designed for the resulting model by HTDPN. Results show that the proposed method is faster in terms of mathematical calculations which can reduce the simulation time and complexity of complicated systems. It would be observed that the proposed approach makes the $PID$ controller design simpler as well. In addition, a comparative study of capsubot has been performed. Simulation results show that the presented method is encouraging compared to the predictive control, which is used in the literature.
Hybrid Petri Nets,Current sample time signals,Capsubot robot,Genetic algorithm
https://mathco.journals.pnu.ac.ir/article_6289.html
https://mathco.journals.pnu.ac.ir/article_6289_4626c84dd36f7fb30dc7a23a22433856.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
3
1
2018
07
01
Best Proximity Point Result for New Type of Contractions in Metric Spaces with a Graph
65
73
EN
Kamal
Fallahi
0000-0003-3400-4424
Department of Mathematics, Payam Noor University, Tehran, Iran.
fallahi1361@gmail.com
10.30473/coam.2019.45808.1112
In this paper, we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph under two different conditions. We then support our main theorem by a non-trivial example and give some consequences of best proximity point of it for usual graphs.
Best proximity point,$G$-continuous mapping,$G$-$varphi$-contraction
https://mathco.journals.pnu.ac.ir/article_6290.html
https://mathco.journals.pnu.ac.ir/article_6290_a9545c3efebf455d12838116880f75ce.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
3
1
2018
07
01
Universal Approximator Property of the Space of Hyperbolic Tangent Functions
75
85
EN
Mohammad Hadi
Noori Skandari
Departement of Applied Mathematics, Shahrood University of Technology, Shahrood, Iran
math.noori@yahoo.com
10.30473/coam.2019.45540.1111
In this paper, first the space of hyperbolic tangent functions is introduced and then the universal<br /> approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.
Hyperbolic tangent functions,Universal approximator,Stabilizer control
https://mathco.journals.pnu.ac.ir/article_6291.html
https://mathco.journals.pnu.ac.ir/article_6291_0da4ef37fc42ca2ddc778439c3d87161.pdf
Payame Noor University (PNU)
Control and Optimization in Applied Mathematics
2383-3130
2538-5615
3
1
2018
07
01
A Higher Order Online Lyapunov-Based Emotional Learning for Rough-Neural Identifiers
87
108
EN
Ghasem
Ahmadi
0000-0003-1331-7253
Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran
g.ahmadi@pnu.ac.ir
Mohammad
Teshnehlab
Department of Control Engineering, K.N. Toosi University of Technology, Tehran, Iran
teshnehlab@eetd.kntu.ac.ir
Fahimeh
Soltanian
Department of Mathematics, Payame Noor University (PNU), P.O. Box, 19395-3697, Tehran, Iran
f_soltanian@pnu.ac.ir
10.30473/coam.2019.40779.1083
o enhance the performances of rough-neural networks (R-NNs) in the system identification,<br /> on the base of emotional learning, a new stable learning algorithm is developed for them. This algorithm facilitates the error convergence by increasing the memory depth of R-NNs. To this end, an emotional signal as a linear combination of identification error and its differences is used to achieve the learning laws.<br /> In addition, the error convergence and the boundedness of predictions and parameters of the model are proved. To illustrate the efficiency of proposed algorithm,<br /> some nonlinear systems including the cement rotary kiln are identified using this method and the results are compared with some other models.
Rough-neural network,System identification,Emotional learning,Lyapunov stability theory
https://mathco.journals.pnu.ac.ir/article_6292.html
https://mathco.journals.pnu.ac.ir/article_6292_b42dbf9ad36d3657c67453806d638088.pdf