A new efficient numerical scheme for solving fractional optimal control problems via a Genocchi operational matrix of integration

Phang, Chang and Ismail, Noratiqah Farhana and Isah, Abdulnasir and Jian , Rong Loh (2018) A new efficient numerical scheme for solving fractional optimal control problems via a Genocchi operational matrix of integration. Journal of Vibration and Control, 24 (14). pp. 3036-3048. ISSN 10775463

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Official URL: DOI:10.1177/1077546317698909

Abstract

In this paper, a new operational matrix of integration is derived using Genocchi polynomials, which is one of the Appell polynomials. By using the matrix, we develop an efficient, direct and new numerical method for solving a class of fractional optimal control problems. The fractional derivative in the dynamic constraints was replaced with the Genocchi polynomials with unknown coefficients and a Genocchi operational matrix of fractional integration. Then, the equation derived from the dynamic constraints was put into the performance index. Hence, the fractional optimal control problems will be reduced to fractional variational problems. By finding a necessary condition for the optimality for the performance index, we will obtain a system of algebraic equations that can be easily solved by using any numerical method. Hence, we obtain the value of unknown coefficients of Genocchi polynomials. Lastly, the solution of the fractional optimal control problems will be obtained. In short, the properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. The approximation approach is simple to use and computer oriented. Illustrative examples are given to show the simplicity, accuracy and applicability of the method.

Item Type:Article
Uncontrolled Keywords:Fractional optimal control problems; Genocchi operational matrix of integration; numerical solution; Caputo fractional derivative; Riemann–Liouville fractional integration
Subjects:Q Science > QA Mathematics > QA273 Probabilities. Mathematical statistics
Divisions:Faculty of Applied Science and Technology > Department of Mathematics and Statistic
ID Code:11190
Deposited By:Mr. Mohammad Shaifulrip Ithnin
Deposited On:13 May 2019 09:12
Last Modified:13 May 2019 09:12

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