A new Legendre operational technique for delay fractional optimal control problems

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• 作者：A. H. Bhrawy ; S. S. Ezz-Eldien
• 关键词：Fractional optimal control problem ; Legendre polynomials ; Caputo definition ; Riemann–Liouville definition ; Operational matrix ; Lagrange multiplier method ; Time delay system
• 刊名：Calcolo
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：53
• 期：4
• 页码：521-543
• 全文大小：668 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Theory of Computation
  
• 出版者：Springer Milan
• ISSN：1126-5434
• 卷排序：53

文摘

In this paper, new operational matrices for shifted Legendre orthonormal polynomial are derived. This polynomial is used as a basis function for developing a new numerical technique for the delay fractional optimal control problem. The fractional integral is described in the Riemann–Liouville sense, while the fractional derivative is described in the Caputo sense. The operational matrix of fractional integrals is used together with the Lagrange multiplier method for the constrained extremum in order to minimize the performance index. The problem is then reduced to a problem consists of a system of easily solvable algebraic equations. Three numerical examples of different types of delay fractional optimal control problems are implemented with their approximate solutions for confirming the high accuracy and applicability of the proposed method.