An approximation method for numerical solution of multi-dimensional feedback delay fractional optimal control problems by Bernstein polynomials

Document Type : Research Article

Authors

• E. Safaie ¹
• M. H. Farahi ²

¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi university of Mashhad, Mashhad, Iran.

² Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi university of Mashhad, Mashhad, Iran, and The center of Excellence on Modelling and Control Systems (CEMCS), Mashhad, Iran.

10.22067/ijnao.v4i1.28711

Abstract

In this paper we present a new method for solving fractional optimal control problems with delays in state and control. This method is based upon Bernstein polynomial basis and using feedback control. The main advantage of using feedback or closed-loop controls is that they can monitor their effect on the system and modify the output accordingly. In this work, we use Bernstein polynomials to transform the fractional time-varying multi-dimensional optimal control system with both state and control delays, into an algabric system in terms of the Bernstein coefficients approximating state and control functions. We use Caputo derivative of degree 0 < a ≤ 1 as the fractional derivative in our work. Finally, some numerical examples are given to illustrate the effectiveness of this method.

Keywords

• Delay fractional optimal control problem
• Caputo fractional derivative
• Bernstein polynomial

20.1001.1.24236977.2014.4.1.5.3

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