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Alavi, Seyyed Ali, Haghighi, Ahmadreza, Yari, Ayatollah, Soltanian, Fahimeh. (1401). A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials. سامانه مدیریت نشریات علمی, 10(3), 755-773. doi: 10.22034/cmde.2021.39419.1728
Seyyed Ali Alavi; Ahmadreza Haghighi; Ayatollah Yari; Fahimeh Soltanian. "A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials". سامانه مدیریت نشریات علمی, 10, 3, 1401, 755-773. doi: 10.22034/cmde.2021.39419.1728
Alavi, Seyyed Ali, Haghighi, Ahmadreza, Yari, Ayatollah, Soltanian, Fahimeh. (1401). 'A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials', سامانه مدیریت نشریات علمی, 10(3), pp. 755-773. doi: 10.22034/cmde.2021.39419.1728
Alavi, Seyyed Ali, Haghighi, Ahmadreza, Yari, Ayatollah, Soltanian, Fahimeh. A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials. سامانه مدیریت نشریات علمی, 1401; 10(3): 755-773. doi: 10.22034/cmde.2021.39419.1728

A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials

Computational Methods for Differential Equations
مقاله 15، دوره 10، شماره 3، مهر 2022، صفحه 755-773    اصل مقاله (487.59 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.39419.1728
نویسندگان
Seyyed Ali Alavi1؛ Ahmadreza Haghighi2؛ Ayatollah Yari* 3؛ Fahimeh Soltanian3
1Department of Mathematics, Payame Noor University, Tehran, Iran.
2Department of Mathematics, Technical and Vocational University, Tehran, Iran.
3Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran.
چکیده
This paper presents a numerical method for solving a class of fractional optimal control problems (FOCPs) based on numerical polynomial approximation. The fractional derivative in the dynamic system is described in the Caputo sense. We used the approach to approximate the state and control functions by the Mott polynomials (M-polynomials). We introduced the operational matrix of fractional Riemann-Liouville integration and apply it to approximate the fractional derivative of the basis. We investigated the convergence of the new method and some examples are included to demonstrate the validity and applicability of the proposed method.
کلیدواژه‌ها
Fractional optimal control problem؛ Caputo derivative؛ Mott polynomials basis؛ Operational matrix
مراجع
  • [1]         O. P. Agrawal, General formulation for the numerical solution of optimal control problems, Int. J. Control, 50(2) (1989), 627–638 .
  • [2]         O. P. Agrawal, A general formulation and solution scheme for fractional optimal control problem, Nonlinear Dynam, 38 (2004), 323–337.
  • [3]         O. P. Agrawal, A quadratic numerical scheme for fractional optimal control problems, Trans. ASME, J. Dyn. Syst. Meas. Control, 130(1) (2008), 011010-011016.
  • [4]         M. Ahmadi Darani and A. Saadatmandi, The operational matrix of fractional derivative of the fractional-order Chebyshev functions and its applications, Computational Methods for Differential Equations, 5(1) (2017), 67-87.
  • [5]         E. Ashpazzadeh and M. Lakestani, Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems, Computational Methods for Differential Equations, 4(2) (2016), 99-115. DOI: 10.1002/oca.2615.
  • [6]         R. L. Bagley and P. J. Torvik, A theoretical basis for the application of fractional calculus to viscoelasticity, J. Rheol., 27 (1983), 201-210.
  • [7]         D. Baleanu, About fractional quantization and fractional variational principles, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), 2520-2523.
  • [8]         T. S. Chow, Fractional dynamics of interfaces between soft-nanoparticles and rough substrates, Phys. Lett. A, 342 (2005), 148-155.
  • [9]         S. S. Ezz-Eldien , E. H. Doha, D. Baleanu, and A. H. Bhrawy, A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems, Journal of Vibration and Control, 23(1) (2017), 16–30.
  • [10]       R. Garrappa, Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial, https://www.mdpi.com/2227-7390/6/2/16/htm, 2018.
  • [11]       I. M. Gelfand and S. V. Fomin, Calculus of Variation (R.A. Silverman, Trans.), PrenticeHall, 1963.
  • [12]       F. Ghomanjani, A numerical technique for solving fractional optimal control problems and fractional Riccati differential equation, Journal of the Egyptian Mathematical Society, 24 (2016), 638–643.
  • [13]       H. Jafari and H. Tajadodi, Fractional order optimal control problems via the operational matrices of bernstein polynomials, U.P.B. Sci. Bull., Series A, 76(3) (2014), 115-128.
  • [14]       S. Jahanshahi and D. F. M. Torres, A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems, J. Optim Theory Appl, 174 (2017), 156–175 .
  • [15]       A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Application of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  • [16]       E. Kreyszig, Introductory Functional Analysis with Applications, New York: John Wiley and sons, (1978).
  • [17]       D. V. Kruchinin, Explicit Formulas for Some Generalized Polynomials, Advenced Studies in Contemporary Math- ematics, 24(3) (2014), 327-332.
  • [18]       A. Lotfi, M. Dehghan, and S. A. Yousefi, A numerical technique for solving fractional optimal control problems, Comput. Math. Appl., 62 (2011), 1055-1067.
  • [19]       R. L. Magin, Fractional calculus in bioengineering, Crit. Rev. Biomed. Eng., 32 (2004), 1-104.
  • [20]       K. Maleknejad and H. Almasieh, Optimal control of Volterra integral equations via triangular functions, Math. Comput. Model., 53 (2011), 1902-1909.
  • [21]       A. Maheswaran and Elango, Characterization of delta operator for euler, Bernoulli of second kind and moot polynomials, International Journal of Pure and Applied Mathematics, 109(2) (2016), 371-384.
  • [22]       M. A. Moghaddam, Y. Edrisi, and M. Lakestani, Solving fractional optimal control problems us- ing Genocchi polynomials, Computational Methods for Differential Equations, 9(1) (2021), 79-93. DOI: 10.22034/cmde.2020.40292.1759.
  • [23]       N. F. Mott, The polarization of electrons by double scattering, Proc.R.Soc.Lond.A., 135 (1932), 429-458.
  • [24]       A. Nemati and S. A. Yousefi, A Numerical Method for Solving Fractional Optimal Control Problems Using Ritz Method, Journal of Computational and Nonlinear Dynamics September, 11/051015(1) (2016).
  • [25]       K. B. Oldham and J. Spanier, The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order, Acad. Press, N. York and London, (1974).
  • [26]       N. O¨ zdemir, O. P. Agrawal, D. Karadeniz, and B. B. Iskender, Fractional optimal control problem of an axis- symmetric diffusion-wave propagation, Phys. Scr, 136 (2009).
  • [27]       I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
  • [28]       E. M. Rabei, K. I. Nawafleh, R. S. Hijjawi, S. I. Muslih, and D. Baleanu, The Hamilton formalism with fractional derivatives, J. Math. Anal. Appl., 327 (2007), 891-897.
  • [29]       S. Roman, The Umbral Calculus, Academic Press, (1984).
  • [30]       T. J. Rivlin, An Introduction to the Approximation of Functions, New York: Dover Publications, 1981.
  • [31]       S. Soradi-Zeid, Solving a class of fractional optimal control problems via a new efficient and accurate method, Computational Methods for Differential Equations, DOI: 10.22034/cmde.2020.35875.1620.
  • [32]       N. H. Sweilam, T. M. AL-Ajmi, and R. H. W. Hoppe, Numerical solution of some types of fractional optimal control problems, Department of Mathematics University of Houston November, 2013.
  • [33]       S. S. Tabatabaei and M. J. Yazdanpanah, Formulation and Numerical Solution for Fractional Order Time Optimal Control Problem Using Pontryagin’s Minimum principle, IFAC PapersOnLine, 50(1) (2017), 9224-9229.
  • [34]       V. Taherpour, M. Nazari, and A. Nemati, A new numerical Bernoulli polynomial method for solving fractional optimal control problems with vector components, Computational Methods for Differential Equations, 9(2) (2021), 446-466. DOI: 10.22034/cmde.2020.34992.1598.
  • [35]       E. Weisstein, Mott Polynomial, From MathWorld–A Wolfram Web Resource, http://mathworld.wolfram.com.
  • [36]       A. Yari, Numerical solution for fractional optimal control problems by Hermite polynomials, Journal of Vibration and Control (2020). DOI: 10.1177/1077546320933129.
  • [37]       S. A. Yousefi, A. Lotfi, and M. Dehghan, The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems, Journal of Vibration and Control Received, 17(13) (2010), 2059–2065.
  • [38]       M. Zamani, M. Karimi-Ghartemani, and N. Sadati, FOPID controller design for robust performance using particle swarm optimization, J. Fract. Calc. Appl. Anal., 10 (2007), 169-188.
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