پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 41 |
| تعداد شماره‌ها | 1,114 |
| تعداد مقالات | 9,532 |
| تعداد مشاهده مقاله | 17,206,567 |
| تعداد دریافت فایل اصل مقاله | 12,040,789 |
A Sub-Ordinary Approach to Achieve Near-Exact Solutions for a Class of Optimal Control Problems | ||
| Control and Optimization in Applied Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 مهر 1403 اصل مقاله (562.17 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2024.70834.1254 | ||
| نویسندگان | ||
| Akbar Hashemi Borzabadi* 1؛ Mohammad Gholami Baladezaei2؛ Morteza Ghachpazan3 | ||
| 1Department of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran. | ||
| 2Department of Mathematics, Damghan Branch, Islamic Azad University, Damghan, Iran. | ||
| 3Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. | ||
| چکیده | ||
| This paper explores the advantages of Sub-ODE strategy in deriving near-exact solutions for a class of linear and nonlinear optimal control problems (OCPs) that can be transformed into nonlinear partial differential equations (PDEs). Recognizing that converting an OCP into differential equations typically increases the complexity by adding constraints, we adopt the Sub-ODE method, as a direct method, thereby negating the need for such transformations to extract near exact solutions. A key advantage of this method is its ability to produce control and state functions that closely resemble the explicit forms of optimal control and state functions. We present results that demonstrate the efficacy of this method through several numerical examples, comparing its performance to various other approaches, thereby illustrating its capability to achieve near-exact solutions. | ||
| کلیدواژه‌ها | ||
| Optimal control problem؛ Subsidiary ordinary differential equation method؛ Parametrization | ||
| مراجع | ||
|
[1] Askenazy, P. (2003). “Symmetry and optimal control in economics”, Journal of Mathematical Analysis and Applications, 282(2), 603-613.
[2] EdrisiTabriz, Y., Lakestani, M.(2015).“ Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions”, Kybernetika, 51(1), 81-89.
[3] 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.
[4] Elnagar, G.N. (1997). “State-control spectral Chebyshev parameterization for linearly constrained quadratic optimal control problems”, Journal of Computational and Applied Mathematics, 79(1), 19-40.
[5] Gachpazan, M., Mortazavi, M. (2015). “Traveling wave solutions for some nonlinear (N + 1)-dimensional evolution equations by using (G′/G) and (1/G′)-expansion methods”, International Journal of Nonlinear Science, 19(3), 137-144.
[6] Gholami Baladezaei, M., Gachpazan, M., Borzabadi, A.H. (2020). “Extraction of approximate solution for a class of nonlinear optimal control problems using 1/G′-expansion technique”, Control and Optimization in Applied Mathematics, 5(2), 65-82.
[7] Highfill, J., McAsey, M.(2001).“An application of optimal control to the economics of recycling”, SIAM Review, 43(4), 679-693.
[8] Kafash, B., Delavarkhalafi, A., Karbassi, S.M. (2012). “Application of Chebyshev polynomials to derive efficient algorithms for the solution of optimal control problems”, Scientia Iranica, 19(3), 795-805.
[9] Kim, H., Sakthivel, R. (2010). “Travelling wave solutions for time-delayed nonlinear evolution equations”, Applied Mathematics Letters, 23(5), 527-532.
[10] Li, L.X., Li, E.Q., Wang, M.L. (2010). “The (G′/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations”, Applied Mathematics-A Journal of Chinese Universities, 25(4), 454-462.
[11] Mehne, H.H., Borzabadi, A.H. (2006). “A numerical method for solving optimal control problems using state parametrization”, Numerical Algorithms, 42(2), 165-169.
[12] 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.
[13] Salam, A., Sharif Uddin, M.D., Dey, P. (2015). “Generalized Bernoulli sub-ODE method and its applications”, Annals of Pure and Applied Mathematics, 10(1), 1-6.
[14] Salama,A.A.(2006).“Numerical methods based on extended one-step methods for solving optimal control problems”, Applied Mathematics and Computation, 183(1), 243-250.
[15] Seierstad, A., Sydsaeter, K. (1986). “Optimal control theory with economic applications”, Elsevier North-Holland, Inc.
[16] Skandari, M.H.N., Tohidi, E. (2011). “Numerical solution of a class of nonlinear optimal control problems using linearization and discretization”, Applied Mathematics, 2(5), 646-652.
[17] Solaymani Fard, O., Borzabadi, A.H. (2007). “Optimal control problem, quasi assignment problem and genetic algorithm”, 422-424.
[18] Tohidi, E., Saberi, Nik, H. (2015). “A Bessel collocation method for solving fractional optimal control problems”, Applied Mathematical Modelling, 39, 455-465.
[19] Tohidi, E., Navid Samadi, O.R., Farahi, M.H. (2011). “Legendre approximation for solving a class of nonlinear optimal control problems”, Journal of Mathematical Finance, 1(1), 8-13.
[20] Wang, M., Li, X., Zhang, J. (2008). “The (G′/G)-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, Fırat University, Turkey.
[22] Zhang, S., Tong, J.L., Wang, W. (2008). “A generalized (G′/G)-expansion method for the mKdV equation with variable coefficients”, Physics Letters A, 372(13), 2254-2257.
[23] Zheng, B.(2011).“A new Bernoulli sub-ODE method for constructing traveling wave solutions for two nonlinear equations with any order”, University Politechnica of Bucharest Scientific Bulletin Series A, 73(3), 85-94.
[24] Zheng, B. (2012). “Application of A generalized Bernoulli sub-ODE method for finding traveling solutions of some nonlinear equations”, WSEAS Transactions on Mathematics, 7(11), 618-626. | ||
|
آمار تعداد مشاهده مقاله: 15 تعداد دریافت فایل اصل مقاله: 15 |
||