An Adaptive Lyapunov-Based Controller for HIV Treatment
Sahar
Vaseei
School of Mathematics and Computer Science, Damghan University, Damghan, Iran.
author
Mohammad Reza
Zarrabi
School of Mathematics and Computer Science, Damghan University, Damghan, Iran.
author
text
article
2020
eng
In view of the tremendous importance of patients’ stability in medical sciences, this paper addresses the application of a sliding mode control in medical devices. In doing so, we consider a nonlinear dynamic system that shows the mathematical model of the human immunodeficiency virus. This nonlinear model has three variable states: healthy cells, infected cells, and free viruses. The proposed controller displays the effect of medication on preventing the production of the virus and blocking the new infection. This controller ensures the stability of this dynamic system provided for HIV in the event of a bounded disturbance. The stability and convergence of this process are proved by the Lyapunov theorem. Finally, a numerical example is given to demonstrate the efficiency of the proposed method.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
5
v.
2
no.
2020
1
10
https://mathco.journals.pnu.ac.ir/article_8163_f5cc888379ff690b5bb5229c3a9af331.pdf
dx.doi.org/10.30473/coam.2021.56157.1153
A Numerical Formulation for N-Dimensional Wave Equations Using Shearlets
Rama
Amiri
Department of Mathematics and Applications,
Faculty of Sciences, University of Mohaghegh Ardabili,
P.O. Box. 11367-56199, Ardabil, Iran.
author
Mohammad
Zarebnia
Department of Mathematics and Applications,
Faculty of Sciences, \ University of Mohaghegh Ardabili,
P.O. Box. 11367-56199, Ardabil, Iran.
author
Reihaneh
Raisi Tousi
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran.
author
text
article
2020
eng
A shearlet frame approach is used to solve $n$-dimensional wave equations numerically. By the presented procedure, the shearlet coefficients are obtained via separate time-independent partial differential equations. The proposed method has the advantage of separation of spatial and temporal parameters. The issues of convergence and best approximation are also discussed.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
5
v.
2
no.
2020
11
24
https://mathco.journals.pnu.ac.ir/article_8164_b5bee6f45b21b8cf34b860d372232a40.pdf
dx.doi.org/10.30473/coam.2021.56816.1157
Application of Fuzzy Logic for Advertising Marketing Campaigns
Abbas
Bashiri
Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-4697, Tehran, Iran.
author
Seyed Mehdi
Mirhosseini-Alizamini
Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-4697, Tehran, Iran.
author
Mohammad Mehdi
Nasrabadi
Department of Mathematics, Payame Noor University (PNU),
P.O. Box. 19395-4697, Tehran, Iran.
author
text
article
2020
eng
Evaluation of advertising marketing campaigns is a very important and complex task, so far no comprehensive model has been presented in this regard. The present study aims to provide a decision framework for evaluating marketing campaigns. This article collects real-world data from an Iranian bank deposit marketing campaign. For this purpose, 250 cases were considered to extract the rules and 60 cases were considered as test data. Information is provided on 15 important parameters of marketing education, defaults, age, occupation, marriage, day, contact, balance, housing, loans, previous contact, previous outcome, month, call duration, and campaigns. A fuzzy expert system was designed with 12 rules after reviewing the rules and removing similar and contradictory rules by using their degree calculation. In this system, by integrating some factors, finally, 6 input variables and one output variable were considered that were used by the product inference engine, singleton fuzzifier, and center average defuzzifier. It was observed that the designed fuzzy expert system provides very good results.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
5
v.
2
no.
2020
25
37
https://mathco.journals.pnu.ac.ir/article_8165_5c06ca8291c8a8e9ec4101a735b847de.pdf
dx.doi.org/10.30473/coam.2021.58392.1160
Adjusting the Coefficients of the PI^α D^β Controllers Using Iterative Feedback Tuning (IFT) Algorithm
Mohammad Ali
Vali
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
author
Mahdi
Mashayekhi Esfichar
Department of Mathematics, Payame, Noor University (PNU), P.O. BOX 19395-4697. Tehran, Iran
author
Shahriar
Farahmand Rad
Department of Mathematics, Payame Noor University (PNU), P.O. BOX 19395-4697, Tehran, Iran
author
text
article
2020
eng
Iterative feedback tuning (IFT) is an algorithm for adjusting the coefficients of the integer-order type proportional-integral-derivative (PID) controllers without needing a system model. The IFT algorithm is performed iteratively with the aim of optimizing the control coefficients at each stage via an objective function. In this research, for the first time, the IFT algorithm is used to adjust all the coefficients of the fractional order PID controllers, i.e., PI^α D^β controllers to have optimal performance. For this purpose, fractional order calculations and the integer-order version of the IFT algorithm are firstly presented, and the novel IFT algorithm is then used to adjust coefficients of the PI^α D^β controller. Finally, the performance of the proposed method is illustrated and verified through some examples.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
5
v.
2
no.
2020
39
64
https://mathco.journals.pnu.ac.ir/article_8166_f51802a4c2a718f7f7e82365ee4e358c.pdf
dx.doi.org/10.30473/coam.2021.56679.1156
Extraction of Approximate Solution for a Class of Nonlinear Optimal Control Problems Using 1/G'-Expansion Technique
Mohammad
Gholami Baladezaei
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
author
Morteza
Gachpazan
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
author
Akbar
Borzabadi
Department of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran
author
text
article
2020
eng
In this paper, the benefits of 1/G'-expansion technique are utilized to create a direct scheme for extracting approximate solutions for a class of optimal control problems. In the given approach, first state and control functions have been parameterized as a power series, which is constructed according to the solutions of a Bernoulli differential equation, where the number of terms in produced power series is determined by the balance method. A proportionate replacement and solving the created optimization problem lead to suitable solutions close to the analytical ones for the main problem. Numerical experiments are given to evaluate the quality of the proposed method.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
5
v.
2
no.
2020
65
82
https://mathco.journals.pnu.ac.ir/article_8167_bc9a6c2e2d9e01857b1c525a26978015.pdf
dx.doi.org/10.30473/coam.2021.59069.1163
Topological Subdifferential and its Role in Nonsmooth Optimization with Quasiconvex Data
Hamed
Soroush
Department of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, Iran
author
text
article
2020
eng
In this paper, we study nonsmooth optimization problems with quasiconvex functions using topological subdifferential. We present some necessary and sufficient optimality conditions and characterize topological pseudoconvex functions. Finally, the Mond-Weir type weak and strong duality results are stated for the problems.
Control and Optimization in Applied Mathematics
Payame Noor University (PNU)
2383-3130
5
v.
2
no.
2020
83
91
https://mathco.journals.pnu.ac.ir/article_8168_05c1544ae253e87fb4dbe39caf6aa0c1.pdf
dx.doi.org/10.30473/coam.2021.59584.1165