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SCW-iterative-computational method for solving a wide class of nonlinear fractional optimal control problems with Caputo derivatives

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  • Baghani, Omid

Abstract

The present paper offers an iterative-computational approach based on left and right operational matrices of the second Chebyshev wavelets (SCWs) in solving nonlinear fractional optimal control problems (FOCPs). The operational matrices are constructed by the hat functions (HFs). We first introduce necessary optimality conditions applying variational methods in a form of fractional two-point boundary value problem (TPBVP). For solving TPBVP, a fixed point iterative sequence, starting with an initial guess, in the hope of achieving more accurate solutions, is suggested. The SCWs-coefficients are easily obtained without any integrating. The order of convergence of the proposed method is accomplished in a new normed space. In the end of the article, some illustrative examples are provided to confirm the ability of the suggested technique.

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  • Baghani, Omid, 2022. "SCW-iterative-computational method for solving a wide class of nonlinear fractional optimal control problems with Caputo derivatives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 540-558.
    • Handle: RePEc:eee:matcom:v:202:y:2022:i:c:p:540-558
    DOI: 10.1016/j.matcom.2022.07.025
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    1. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Jahanshahi, Hadi & Orozco-López, Onofre & Munoz-Pacheco, Jesus M. & Alotaibi, Naif D. & Volos, Christos & Wang, Zhen & Sevilla-Escoboza, R. & Chu, Yu-Ming, 2021. "Simulation and experimental validation of a non-equilibrium chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    4. Baghani, Omid, 2021. "Second Chebyshev wavelets (SCWs) method for solving finite-time fractional linear quadratic optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 343-361.
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