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A New Approach for Solving Optimal Control Problem by Using Orthogonal Function

  • Akram KheirabadiEmail author
  • Asadollah Mahmoudzadeh Vaziri
  • Sohrab Effati
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)

Abstract

In the present paper we introduce a numerical technique for solving fractional optimal control problems (FOCP) based on an orthonormal wavelet. First we approximate the involved functions by Sine-Cosine wavelet basis; then, an operational matrix is used to transfer the given problem in to a linear system of algebraic equations. In fact operational matrix of the Riemann-Liouville fractional integration and derivative of Sine-Cosine wavelet are employed to achieve a linear algebraic equation, in place of the dynamical system in terms of the unknown coefficients. The solution of this system, gives us the solution of original problem. A numerical example is also given.

Keywords

Fractional optimal control problem Sine-Cosine wavelet Operational matrix Caputo derivative Riemann-Liouville fractional integration 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Akram Kheirabadi
    • 1
    Email author
  • Asadollah Mahmoudzadeh Vaziri
    • 1
  • Sohrab Effati
    • 2
  1. 1.Department of Mathematics, Faculty of Mathematical Science and StatisticsUniversity of BirjandBirjandIran
  2. 2.Department of Applied Mathematics, Faculty of Mathematical Science and StatisticsFerdowsi University of MashhadMashhadIran

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