A new class of orthonormal basis functions: application for fractional optimal control problems. Issue 2 (25th January 2022)

• Record Type: Journal Article
• Authors: Heydari, M. H.; Razzaghi, M.
• Is Part Of: International journal of systems science. Volume 53:Issue 2(2022)
• Page Start: 240
• Page End: 252
• Publication Date: 2022-01-25
• Subjects: Orthonormal piecewise Chelyshkov functions -- fractional optimal control problems -- fractional integral matrix; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2021.1947411
• Languages: English
• ISSNs: 0020-7721

Abstract

Abstract : This study aims to generate a novel set of basis functions called the orthonormal piecewise Chelyshkov functions to solve a certain category of optimal control problems whose dynamical system is governed by a nonlinear fractional differential equation. A new fractional integral matrix associated with these basis functions is derived. This matrix significantly reduces the computations in solving such problems. The proposed approach transforms the original problem into a nonlinear programming one by expanding the control and state variables in terms of the orthonormal piecewise Chelyshkov functions and employing the derived fractional integral matrix. Some numerical problems are examined for verification of the proposed method.