Pseudospectral method for fractional infinite horizon optimal control problems. (6th August 2020)

• Record Type: Journal Article
• Authors: Yang, Yin; Noori Skandari, M. H.
• Other Names: Yuan Shuai guestEditor.; Wan Yimin guestEditor.; Zhang Lixian guestEditor.; Baldi Simone guestEditor.
• Is Part Of: Optimal control applications and methods. Volume 41:Number 6(2020)
• Page Start: 2201
• Page End: 2212
• Publication Date: 2020-08-06
• Subjects: Caputo fractional derivative -- fractional infinite horizon optimal control -- nonlinear programming -- shifted Legendre pseudospectral method; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2649
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: Up to now, several numerical methods have been presented to solve finite horizon fractional optimal control problems by researchers, while solving fractional optimal control problems on infinite domain is a challenging work. Hence, in this article, a numerical method is proposed to solve fractional infinite horizon optimal control problems. At the first stage, a domain transformation technique is used to map the infinite domain to a finite horizon. Also, fractional derivative defined on an unbounded domain is converted into an equivalent derivative on a finite domain. Then, a new shifted Legendre pseudospectral method is utilized to solve the obtained finite problem and a nonlinear programming problem is suggested to approximate the optimal solutions. Finally, some numerical examples are given to show the efficiency of the method.