Hybrid Functions to Solve Fractional Optimal Control Problems Using the Collocation Method
Publish place: International Journal of Industrial Electronics, Control and Optimization، Vol: 4، Issue: 3
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IECO-4-3_004
تاریخ نمایه سازی: 20 تیر 1401
Abstract:
This article aims to introduce a modern numerical method based on the hybrid functions, consisting of the Bernoulli polynomials and Block-Pulse functions. An indirect approach is proposed for solving the fractional optimal control problems (FOCPs). Firstly, the two-point boundary value problem (TPBVP) is calculated for a class of FOCPs, including integer-fractional derivatives, leading to a system of fractional differential equations (FDEs), which have the left and right-sided Caputo fractional derivatives (CFD). Therefore, a new approach is proposing to achieve the left Riemann-Liouville fractional integral (LRLFI) and right Riemann-Liouville fractional integral (RRLFI) operators for Bernoulli hybrid functions. Then, hybrid functions approximation, LRLFI, and RRLFI operators, and the collocation method are used to solve the TPBVP. The error bounds for the hybrid function and LRLFI and RRLFI operators are also presented. Moreover, the convergence of the proposed method is proved. Finally, the simplicity and accuracy of the method are illustrated using some numerical examples.
Keywords:
Bernoulli Hybrid functions , Fractional optimal control , Riemann-Liouville fractional Integral operators. Collocation method
Authors
Seyed Mehdi Shafiof
Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran
Javad Askari Marnani
Faculty of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran
Maryam Shamssolary
Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran
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