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Extraction of Approximate Solution for a Class of Nonlinear Optimal Control Problems Using 1/G'-Expansion Technique | ||
| Control and Optimization in Applied Mathematics | ||
| دوره 5، شماره 2، مهر 2020، صفحه 65-82 اصل مقاله (776.86 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2021.59069.1163 | ||
| نویسندگان | ||
| Mohammad Gholami Baladezaei1؛ Morteza Gachpazan* 2؛ Akbar Hashemi Borzabadi3 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. | ||
| 2Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| 3Department of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Optimal control problem؛ 1/G'-Expansion method؛ Parametrization | ||
| مراجع | ||
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[1] Abdus Salam M., Sharifuddin M., Dey P. 2015. “Generalized Bernoulli Sub-ODE method and its applications”, Annals of Pure and Applied Mathematics, 10(1), 1-6.
[2] Al-Mamun A., Ananna S. N., An T., Shahen N. H., Foyjonnesa M. 2021. “Periodic and solitary wave solutions to a family of new 3D fractional WBBM equations using the twovariable method”, Partial Differential Equations in Applied Mathematics, 3, 1-9.
[3] Edrisi Tabriz Y., Lakestani M. 2015. “Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions”, Kybernetika, 51(1), 81-89.
[4] Effati S., Pakdaman M. 2012. “Optimal control problem via neural networks”, Neural Computing & Applications, 23, 2093-2100.
[5] El-Gindy T. M., El-Hawary H. M., Salim M. S., El-Kady M. 1995. “A Chebyshev approximation for solving optimal control problems”, Computers & Mathematics with Applications, 29(6), 35-45.
[6] El-Kady M., Elbarbary E. M. E. 2002. “A Chebyshev expansion method for solving nonlinear optimal control problems”, Applied Mathematics and Computation, 129, 171-182.
[7] Fard O. S., Borzabadi A. H. 2007. “Optimal control problem, quasi-assignment problem and genetic algorithm”, International Journal of Mathematical and Computational Sciences, 1(9), 402-404.
[8] Gachpazan M., Mortazavi M. 2015. “Traveling wave solutions for Some nonlinear (N + 1)-dimensional evolution equations by using (GG′ ) and (G1′ )-expansion methods”, International Journal of Nonlinear Science, 19(3), 137-144.
[9] Hua H. 2000. “Numerical solution of optimal control problems”, Optimal Control Applications and Methods, 21, 233-241.
[10] Ibrahim F., Hattaf K., Rihan F. A., Turek S. 2017. “Numerical method based on extended one-step schemes for optimal control problem with time-lags”, International Journal of Dynamics and Control, 5, 1172-1181.
[11] Kafash B., Delavarkhalafi A. 2015. “Restarted State Parameterization Method for Optimal Control Problems”, Journal of Mathematics and Computer Science, 14, 151-161.
[12] Kafash B., Delavarkhalafi A., Karbassi SM. 2012. “Application of Chebyshev polynomials to derive effcient algorithms for the solution of optimal control problems”, Scientia Iranica, 19(3), 795-805.
[13] Li L. X., Li E. Q., Wang M. L. 2010. “The (GG′ , G1 )-expansion method and its application to travelling wave solutions of the Zakharov equations”, Applied Mathematics-A Journal of Chinese Universities, 25, 454-462.
[14] Mehne H. H., Borzabadi A. H. 2006. “A numerical method for solving optimal control problems using state parametrization”, Numerical Algorithms, 42(2), 165-169.
[15] Pham H. 2018. “A logistic fault-dependent detection software reliability model”, Journal of Universal Computer Science, 24(12), 1717-1730.
[16] Pinch E. R. 1993. “Optimal Control and the Calculus of Variations”, Cxford University Press.
[17] Rafiei Z., Kafash B., Karbassi S. M. 2017. “A computational method for solving optimal control problems and their applications”, Control and Optimization in Applied Mathematics, 2(1), 1-13.
[18] Shirazian M., Effati S. 2013. “Feedback controller design for linear and a class of nonlinear optimal control problems”, Optimal Control Applications and Methods, 35(3), 271-285. [19] Spangelo I. 1994. “Trajectory optimization for vehicles using control parametrization and nonlinear programming”, Ph.D. thesis.
[20] Wang M., Li X., Zhang J. 2008. “The (GG′ )-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics”, Physics Letters A, 372(4), 417- 423.
[21] Yokus A. 2011. “Solutions of some nonlinear partial differential equations and comparison of their solutions”, Ph.D. Thesis, Firat University, Elazig.
[22] Yokus A., Durur H. 2019. “Complex hyperbolic traveling wave solutions of Kuramoto Sivashinsky equation using (1/G′)-expansion method for nonlinear dynamic theory”, Journal of Institute of Science and Technology, 21(2), 590-599.
[23] Yokus A., Durur H., Ahmad H., Thounthong P., Zhang Y. F. 2020. “Construction of exact traveling wave solutions of the Bogoyavlenskii equation by (G/G ,1/G)-expansion and ( 1/G)-expansion techniques”, Results in Physics, 19, 1-8.
[24] Zheng B. 2011. “A new Bernoulli Sub-ODE method for constructing traveling wave solutions for two nonlinear equations with any order”, UPB Scientific Bulletin, Series A, 73(3), 85-94.
[25] Zheng B. 2012. “Application of a generalized Bernoulli Sub-ODE method for finding traveling solutions of some nonlinear equations”, Wseas Transactions on Mathematics, 11(7), 618-626.
[26] Zhang S., Tong J., Wang W. 2008. “A generalized (GG′)-expansion method for the mKdV equation with variable coefficients”, Physics Letters A, 372(13), 2254-2257. | ||
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