An approximate method for solving fractional optimal control problems by the hybrid of block‐pulse functions and Taylor polynomials. (13th December 2017)

• Record Type: Journal Article
• Authors: Yonthanthum, W.; Rattana, A.; Razzaghi, M.
• Other Names: Chachuat Benoît guestEditor.; Sager Sebastian guestEditor.
• Is Part Of: Optimal control applications and methods. Volume 39:Number 2(2018)
• Page Start: 873
• Page End: 887
• Publication Date: 2017-12-13
• Subjects: block pulse -- Caputo derivative -- fractional optimal control -- hybrid functions -- Taylor basis; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2383
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: In this paper, an efficient and accurate computational method based on the hybrid of block‐pulse functions and Taylor polynomials is proposed for solving a class of fractional optimal control problems. In the proposed method, the Riemann‐Liouville fractional integral operator for the hybrid of block‐pulse functions and Taylor polynomials is given. By taking into account the property of this operator, the solution of fractional optimal control problems under consideration is reduced to a nonlinear programming one to which existing well‐developed algorithms may be applied. The present method applies to both fractional optimal control problems with or without inequality constraints. The method is computationally very attractive and gives very accurate results. Easy implementation and simple operations are the essential features of the proposed hybrid functions. Illustrative examples are given to assess the effectiveness of the developed approximation technique.