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A Semi-Analytic Method for Solving a Class of Non-Linear Optimal Control Problems | ||
| International Journal of Industrial Electronics Control and Optimization | ||
| مقاله 2، دوره 3، شماره 4، آذر 2020، صفحه 415-429 اصل مقاله (869.45 K) | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22111/ieco.2020.32367.1225 | ||
| نویسندگان | ||
| Maryam Alipour* 1؛ Pooneh Omidiniya2 | ||
| 1Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran | ||
| 2Department of Mathematics, Statistics and Computer Science, University of Sistan and Baluchestan, Zahedan, Iran. | ||
| چکیده | ||
| This paper, proposes an approximate analytical method to solve a class of optimal control problems. This method is an enhancement of the variational iteration method (VIM) which is called modifi ed variational iteration method (MVIM) and eliminates all additional calculations in VIM, thus requires less time to do the calculations. In this approach, first, the optimal control problem is converted into a non-linear two-point boundary value problem via the Pontryagins maximum principle, and then we applied the MVIM method to solve this boundary value problem. This suggested method is suitable for a large class of non-linear optimal control problems that for the non-linear part of the problem, we used the Taylor series expansion. In the end, three examples are provided to demonstrate the simplicity and efficiency of the method. The numerical results of the proposed method versus other methods are presented in tables. All calculations were carried out using Mathematica software. | ||
| کلیدواژهها | ||
| Modifi ed variational iteration method (MVIM)؛ Differential equations؛ Optimal control problems؛ Numerical solution | ||
| مراجع | ||
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[1] W. L. Garrard, J. M. Jordan, “Design of nonlinear automatic flight control systems,” Automatica, 13, 497 - 505, 1977. [2] J. L. Junkins and J. D. Turner, “Optimal Spacecraft Rotational Maneuvers,” Elsevier, Amsterdam, 1986. [3] M. Itik, M. U. Salamci, S. P. Banksa, “Optimal control of drug therapy in cancer treatment,” Nonlinear Analysis, 71 (12), 1473 - 1486, 2009. [4] S. Wei, M. Zefran, R. A. Decarlo, “Optimal control of the robotic system with logical constraints., application to UAV path planning,” Proceeding(s) of the IEEE International Conference on Robotics and Automation, Pasadena, CA, USA, (2008). [5] M. Alipour, M. A. Vali, A. H. Borzabadi, “A direct approach for approximate optimal control of integro differential equations based on homotopy analysis and parametrization method,” IMA Journal of Mathematical Control and Information, 34, 611 - 630, 2017. [6] E. Tohidi, O. R. N. Samadi, “Legendre spectral collocation method for approximating the solution of shortest path problems,” Syst. Sci. Control Eng, 3, 62 - 68, 2014. [7] M. Shirazian, and S. Effati, “Solving a Class of Nonlinear Optimal Control Problems via He’s Variational Iteration Method,”International Journal of Control, Automation, and Systems, 10, 249 - 256, 2012. [8] B. Kafash, A. Delavarkhalafi, S. MKarbassi, K. Boubaker. “A Numerical Approach for Solving Optimal Control Problems Using the Boubaker Polynomials Expansion Scheme,” Journal of Interpolation and Approximation in Scientific Computing, 2014, 1 - 18, 2014. [9] M. Matinfar, and M. Saeidy, “A new analytical method for solving a class of nonlinear optimal control problems,” Optimal Control Applications and Methods, 35, 286 - 302, 2014. [10] H. Jafari, S. Ghasempour, D. Baleanu, “On comparison between iterative methods for solving nonlinear optimal control problems,” Journal of Vibration and Control, 22, 2281 - 2287, 2016. [11] M. Alipour, M. A. Vali, A. H. Borzabadi, “A hybrid parametrization approach for a class of nonlinear optimal control problems,” Numerical Algebra, Control and Optimization, 9, 493 - 506, 2019. [12] A. Jajarmi, N. Pariz, A. Vahidian Kamyad, S. Effati. “A highly computational efficient method to solve nonlinear optimal control problems,” Scientia Iranica, 19, 759 - 766, 2012. [13] Z. Shabani, H. Tajadodi, “A numerical scheme for constrained optimal control problems,” International Journal of Industrial Electronics, Control and Optimization, 2, 233 - 238, 2019. [14] H. Saberi Nik, S. Effati, S. S. Motsa, M. Shirazian, “Spectral homotopy analysis method and its convergence for solving a class of nonlinear optimal control problems,” Numer Algor, 65, 171 - 194, 2014. [15] M. Akbarian, N. Eghbal2, N. Pariz, “A Novel Method for Optimal Control of Piecewise Affine Systems Using Semi-Definite Programming,” International Journal of Industrial Electronics, Control and Optimization, 3, 59 - 68, 2020. [16] M. Dehghan, M. Abbaszadeh, “The solution of nonlinear Green - Naghdi equation arising in water sciences via a meshless method which combines moving kriging interpolation shape functions with the weighted essentially non - oscillatory method,” Communications in Nonlinear Science and Numerical Simulation, 68, 220 - 239, 2019. [17] E. Zakeri, S. Farahat, S. A. Moezi, A. Zare, “Path planning for unmanned underwater vehicle in 3d space with obstacles using spline-imperialist competitive algorithm and optimal interval type-2 fuzzy logic controller,” Latin American Journal of Solids and Structures, 13, 1054 - 1085, 2016. [18] E. Zakeri, S. A. Moezi, M. Eghtesad, “Tracking control of ball on sphere system using tuned fuzzy sliding mode controller based on artificial bee colony algorithm,” International Journal of Fuzzy Systems, 20, 295 - 308, 2018. [19] E. Zakeri, S. A. Moezi, M. Eghtesad, “Optimal interval type-2 fuzzy fractional order super twisting algorithm: A second order sliding mode controller for fully-actuated and under-actuated nonlinear systems,” ISA transactions, 85, 13 - 32, 2019. [20] J.H. He, “A new approach to nonlinear partial differential equations,” Commun. Nonlinear Sci. Numer. Simulation., 2 (4), 230 - 235, 1997. [21] J.H. He, “Variational iteration method - A kind of non- linear analytical technique: Some examples,” International Journal of Non-Linear Mechanics, 34, 699 - 708, 1999. [22] T. A. Abassy, M. A. El-Tawil, H. El-Zoheiry, “Modified variational iteration method for Boussinesq equation,” Computers, and Mathematics with Applications, 54 (7 - 8), 955 - 965, 2007. [23] A. Jajarmi, N. Pariz, A. V. Kamyad, and S. Effati, “A novel modal series representation approach to solve a class of nonlinear optimal control problems,” International Journal of Innovative Computing, Information and Control, 7, 1413 - 1425, 2011. [24] J. E. Rubio, “Control and Optimization, the Linear Treatment of Nonlinear Problems,” Manchester University Press, Manchester, UK, 1986. | ||
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