An Efficient Algorithm for the Multi-Scale Solution of Nonlinear Fractional Optimal Control Problems

Araz Noori Dalawi, Mehrdad Lakestani () and Elmira Ashpazzadeh
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Araz Noori Dalawi: Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz 5166616471, Iran
Mehrdad Lakestani: Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz 5166616471, Iran
Elmira Ashpazzadeh: Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz 5166616471, Iran

Mathematics, 2022, vol. 10, issue 20, 1-16

Abstract: An efficient algorithm based on the wavelet collocation method is introduced in order to solve nonlinear fractional optimal control problems (FOCPs) with inequality constraints. By using the interpolation properties of Hermite cubic spline functions, we construct an operational matrix of the Caputo fractional derivative for the first time. Using this matrix, we reduce the nonlinear fractional optimal control problem to a nonlinear programming problem that can be solved with some suitable optimization algorithms. Illustrative examples are examined to demonstrate the important features of the new method.

Keywords: fractional-order optimal control; Caputo fractional derivative; Riemann–Liouville fractional integration; biorthogonal Hermite cubic spline multiscaling bases (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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