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Second Chebyshev wavelets (SCWs) method for solving finite-time fractional linear quadratic optimal control problems

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  • Baghani, Omid

Abstract

In this paper, we present an indirect computational procedure based on the truncated second kind Chebyshev wavelets for finding the solutions of Caputo fractional time-invariant linear optimal control systems which the functional cost consists of the finite-time quadratic cost function. Utilizing the operational matrices of second Chebyshev wavelets (SCWs) of the Riemann–Liouville fractional integral, the corresponding linear two-point boundary value problem (TPBVP), obtained from the fractional Euler–Lagrange equations, is reduced to a coupled Sylvester-type matrix equation. An equivalent linear matrix form using the Kronecker product is constructed. The upper bound of the error of the SCWs approximation and the convergence of the proposed method are investigated. Low computational complexity and flexible accuracy are two important superiorities of this approach. Numerical experiments provide satisfactory results compared to the exiting techniques.

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  • 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.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:343-361
    DOI: 10.1016/j.matcom.2021.05.017
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    1. Wang, Yanxin & Zhu, Li, 2016. "SCW method for solving the fractional integro-differential equations with a weakly singular kernel," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 72-80.
    2. H. Saberi Nik & Sohrab Effati & Sandile S. Motsa & Stanford Shateyi, 2013. "A New Piecewise-Spectral Homotopy Analysis Method for Solving Chaotic Systems of Initial Value Problems," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-13, April.
    3. Zhu, Li & Wang, Yanxin, 2015. "Numerical solutions of Volterra integral equation with weakly singular kernel using SCW method," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 63-70.
    4. 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.
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    1. 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.

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