Generalized Bernoulli Polynomials: Solving Nonlinear 2D Fractional Optimal Control Problems

被引：0
作者：
H. Hassani
J. A. Tenreiro Machado
Z. Avazzadeh
E. Naraghirad
M. Sh. Dahaghin
机构：
[1] Ton Duc Thang University,Faculty of Mathematics and Statistics
[2] Polytechnic of Porto,Department of Electrical Engineering, Institute of Engineering
[3] Xi’an Jiaotong-Liverpool University,Laboratory for Intelligent Computing and Financial Technology, Department of Mathematical Science
[4] Yasouj University,Department of Mathematics
[5] Shahrekord University,Faculty of Mathematics
来源：
Journal of Scientific Computing | 2020年 / 83卷
关键词：
Generalized Bernoulli polynomials; Nonlinear 2-dim fractional optimal control problems; Nonlinear fractional dynamical systems; Goursat–Darboux conditions; Fractional derivative; Coefficients and parameters; 93C20; 49J20; 35C10;
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摘要：
This work develops an optimization method based on a new class of basis function, namely the generalized Bernoulli polynomials (GBP), to solve a class of nonlinear 2-dim fractional optimal control problems. The problem is generated by nonlinear fractional dynamical systems with fractional derivative in the Caputo type and the Goursat–Darboux conditions. First, we use the GBP to approximate the state and control variables with unknown coefficients and parameters. Afterwards, we substitute the obtained values for the variables and parameters in the objective function, nonlinear fractional dynamical system and Goursat–Darboux conditions. The 2-dim Gauss–Legendre quadrature rule together with a fractional operational matrix construct a constrained problem, that is solved by the Lagrange multipliers method. The convergence of the GBP method is proved and its efficiency is demonstrated by several examples.
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