Collocation method to solve inequality-constrained optimal control problems of arbitrary order

  • K. RabieiEmail author
  • K. Parand
Original Article


In this paper, the generalized fractional order of the Chebyshev functions (GFCFs) based on the classical Chebyshev polynomials of the first kind is used to obtain the solution of optimal control problems governed by inequality constraints. For this purpose positive slack functions are added to inequality conditions and then the operational matrix for the fractional derivative in the Caputo sense, reduces the problems to those of solving a system of algebraic equations. It is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach one. The applicability and validity of the method are shown by numerical results of some examples, moreover a comparison with the existing results shows the preference of this method.


Optimal control problems Fractional calculus Chebyshev functions Operational matrix Convergence analysis 



We have to express our appreciation to the reviewers for their helpful comments which improve the quality of this work.


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer SciencesShahid Beheshti University, G.CTehranIran
  2. 2.Department of Cognitive Modelling, Cognitive and Brain SciencesShahid Beheshti University, G.CTehranIran

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