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Alipour, Maryam, Soradi Zeid, Samaneh. (1401). Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method. سامانه مدیریت نشریات علمی, 11(1), 52-64. doi: 10.22034/cmde.2022.50643.2100
Maryam Alipour; Samaneh Soradi Zeid. "Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method". سامانه مدیریت نشریات علمی, 11, 1, 1401, 52-64. doi: 10.22034/cmde.2022.50643.2100
Alipour, Maryam, Soradi Zeid, Samaneh. (1401). 'Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method', سامانه مدیریت نشریات علمی, 11(1), pp. 52-64. doi: 10.22034/cmde.2022.50643.2100
Alipour, Maryam, Soradi Zeid, Samaneh. Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method. سامانه مدیریت نشریات علمی, 1401; 11(1): 52-64. doi: 10.22034/cmde.2022.50643.2100

Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method

Computational Methods for Differential Equations
مقاله 5، دوره 11، شماره 1، فروردین 2023، صفحه 52-64    اصل مقاله (542.92 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50643.2100
نویسندگان
Maryam Alipour1؛ Samaneh Soradi Zeid* 2
1Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
2Faculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan, Iran.
چکیده
In this paper, we introduce a new direct scheme based on Dickson polynomials and collocation points to solve a class of optimal control problems (OCPs) governed by Volterra integro-differential equations namely Volterra integro-OCPs (VI-OCPs). This topic requires to calculating the corresponding operational matrices for expanding the solution of this problem in terms of Dickson polynomials. Further, the highlighted method allows us to transform the VI-OCP into a system of algebraic equations for choosing the coefficients and control parameters optimally. The error estimation of this technique is also investigated which given the high efficiency of the Dickson polynomials to deal with these problems. Finally, some examples are brought to confirm the validity and applicability of this approach in comparison with those obtained from other methods. 
کلیدواژه‌ها
Dickson polynomials؛ Optimal control problem؛ Volterra integro-differential equation؛ Algebraic equations؛ Collocation points؛ Error estimation
مراجع
  • [1] M. Alipour, M. A. Vali, and A. H. Borzabadi, A direct approach for approximate optimal control of integro- differential equations based on homotopy analysis and parameterization method, IMA J. Math. Control Inf., 34(2) (2017), 611–630.
  • [2] M. Alipour and S. Soradi-Zeid, Optimal control of time delay Fredholm integro-differential equations, J. Math. Model., 9(2) (2021), 277–291.
  • [3] S. A. Belbas, A reduction method for optimal control of Volterra integral equations, Appl. Math. Comput., 197(2) (2008), 880–890.
  • [4] A. Blokhuis, X. Cao, W. S. Chou, and X. D. Hou, On the roots of certain Dickson polynomials, J. Number Theory, 188 (2018), 229–246.
  • [5] O. Cots, J. Gergaud, and D. Goubinat, Direct and indirect methods in optimal control with state constraints and the climbing trajectory of an aircraft, Optim. Control. Appl. Methods, 39(1) (2018), 281–301.
  • [6] R. Cont and E. Voltchkova, Integro-differential equations for option prices in exponential Levy models, Finance Stochastics, 9(3) (2005), 299–325.
  • [7] W. S. Chou, The factorization of Dickson polynomials over finite fields, Finite Fields Appl., 3(1) (1997), 84–96.
  • [8] S. B. Chen, S. Soradi-Zeid, M. Alipour, Y. M. Chu, J. F. Gomez-Aguilar, and H. Jahanshahi, Optimal control of nonlinear time-delay fractional differential equations with Dickson polynomials, Fractals, 29(4) (2021), 2150079– 270.
  • [9] L. E. Dickson, The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group, Annal. Math., 11(1/6) (1896), 65–120.
  • [10] A. Diene and M. A. Salim, Fixed points of the Dickson polynomials of the second kind, J. Appl. Math., 2013.
  • [11] M. I. Kamien and E. Muller, Optimal control with integral state equations, The Review of Economic Studies, 43(3) (1976), 469–473.
  • [12] O¨ . K. Ku¨rkcu¨, E. Aslan, and M. Sezer, A numerical approach with error estimation to solve general integro- differential-difference equations using Dickson polynomials, App. Math. Comput., 276 (2016), 324-339.
  • [13] O¨ . K. Ku¨rkcu¨, E. Aslan and M. Sezer, A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials, Sains Malays, 46 (2017), 335–347.
  • [14] O¨ . K. Ku¨rkcu¨, E. Aslan, and M. Sezer, A numerical method for solving some model problems arising in science and convergence analysis based on residual function, App. Num. Math., 121 (2017), 134–148.
  • [15] P. Khodabakhshi and J. N. Reddy, A unified integro-differential nonlocal model, Int. J. Engineering Sci., 95 (2015), 60–75.
  • [16] M. Lakestani and M. Dehghan, Numerical solution of fourth-order integro-differential equations using Chebyshev cardinal functions, Int. J. Comput. Math., 87(6) (2010), 1389–1394.
  • [17] R. Lidl, G. L. Mullen, and G. Turnwald, Dickson polynomials, 65, Chapman and Hall/CRC, 1993.
  • [18] N. Mahmoodi Darani, Hybrid collocation method for some classes of second-kind nonlinear weakly singular integral equation, Comput. Methods Differ. Equ., 2022.
  • [19] J. Ma and G. Ge, A note on permutation polynomials over finite fields, Finite Fields Appl., 48 (2017), 261–270.
  • [20] K. Maleknejad and H. Almasieh, Optimal control of Volterra integral equations via triangular functions, Math.comput. model., 53(9-10) (2011), 1902–1909.
  • [21] K. Maleknejad and A. Ebrahimzadeh, The use of rationalized Haar wavelet collocation method for solving optimal control of Volterra integral equations, J. Vib. Control, 21(10) (2015), 1958–1967.
  • [22] S. Mashayekhi, Y. Ordokhani, and M. Razzaghi, Hybrid functions approach for optimal control of systems described by integro-differential equations, Appl. Math. Model. 37(5) (2013), 3355–3368.
  • [23] H. Mirinejad and T. Inanc, An RBF collocation method for solving optimal control problems, Rob. Auton. Syst., 87 (2017), 219–225.
  • [24] A. S. Matveev and A. V. Savkin, Application of optimal control theory to analysis of cancer chemotherapy regimens, Syst. control lett., 46(5) (2002), 311–321.
  • [25] J. Medlock and M. Kot, Spreading disease: integro-differential equations old and new, Math. biosciences, 184(2) (2003), 201–222.
  • [26] N. Negarchi and K. Nouri, A New Direct Method for Solving Optimal Control Problem of Nonlinear Volterra- Fredholm Integral Equation via the Muntz-Legendre Polynomials, Bulletin of the Iranian Math. Society, 45(3) (2019), 917–934.
  • [27] C. J. Oates, T. Papamarkou, and M. Girolami, The controlled thermodynamic integral for Bayesian model evidence evaluation, J. Am. Stat. Assoc., 111(514) (2016), 634–645.
  • [28] B. Pan, Y. Ma, and Y. Ni, A new fractional homotopy method for solving nonlinear optimal control problems, Acta Astronaut., 161 (2019), 12–23.
  • [29] N. Patel and N. Padhiyar, Modified genetic algorithm using Box Complex method: Application to optimal control problems, J. Process Control, 26 (2015), 35–50.
  • [30] S. Paseban Hag, E. Osgooei, and E. Ashpazzadeh, Alpert wavelet system for solving fractional nonlinear Fredholm integro-differential equations, Comput. Methods Differ. Equ., 9(3) (2021), 762–773.
  • [31] A. V. Rao, A survey of numerical methods for optimal control, Adv. Astronaut. Sci., 135(1) (2009), 497–528.
  • [32] Z. Shabani and H.Tajadodi, A numerical scheme for constrained optimal control problems, Int. J. Ind. Electron. Control Optim., 2(3) (2019), 233–238.
  • [33] T. Stoll, Complete decomposition of Dickson-type recursive polynomials and a related Diophantine equation, For- mal Power Series and Algebraic Combinatorics, Tianjin, China, 2007.
  • [34] E. Safaie, M. H. Farahi, and M. F. Ardehaie, An approximate method for numerically solving multi-dimensional delay fractional optimal control problems by Bernstein polynomials, Comput. Appl. Math., 34(3) (2015), 831–846.
  • [35] G. Tang and K. Hauser, A data-driven indirect method for nonlinear optimal control, Astrodynamics, 3(4) (2019), 345–359.
  • [36] E. Tohidi and O. R. N. Samadi, Optimal control of nonlinear Volterra integral equations via Legendre polynomials, IMA J. Math. Control Inf., 30(1) (2013), 67–83.
  • [37] Q. Wang and J. L. Yucas, Dickson polynomials over finite fields, Finite Fields Appl., 18(4) (2012), 814–831.
  • [38] P. Wei, X. Liao, and K. W. Wong, Key exchange based on Dickson polynomials over finite field with 2m, JCP, 6(12) (2011), 2546–2551.
  • [39] E. M. Yong, L. Chen, and G. J. Tang, A survey of numerical methods for trajectory optimization of spacecraft, J. Astronaut., 29(2) (2008), 397–406.
  • [40] S. Yu¨zbasi and N. Ismailov, An operational matrix method for solving linear Fredholm-Volterra integro-differential equations, Turkish J. Math., 42(1) (2018), 243–256.
  • [41] S. Yu¨zbasi, An exponential method to solve linear Fredholm-Volterra integro-differential equations and residual improvement, Turkish J. Math., 42(5) (2018), 2546–2562.
  • [42] S. Yu¨zbasi, A shifted Legendre method for solving a population model and delay linear Volterra integro-differential equations, Int. J. Biomath., 10(07) (2017), 1750091.
  • [43] S. Yu¨zbasi and M. Sezer, An exponential approach for the system of nonlinear delay integro-differential equations describing biological species living together, Neural Comput. Appl., 27(3) (2016), 769–779.
  • [44] S. Yu¨zbasi, A collocation method based on Bernstein polynomials to solve nonlinear Fredholm-Volterra integro- differential equations, Appl. Math. Comput., 273 (2016), 142–154.
  • [45] S. Yu¨zbasi, Improved Bessel collocation method for linear Volterra integro-differential equations with piecewise intervals and application of a Volterra population model, Appl. Math. Modell., 40 (9-10) (2016), 5349–5363.
  • [46] S. Yu¨zbasi, Numerical solutions of system of linear Fredholm-Volterra integro-differential equations by the Bessel collocation method and error estimation, Appl. Math. Comput., 250 (2015), 320–338.
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