2021
DOI: 10.1177/01423312211047033
|View full text |Cite
|
Sign up to set email alerts
|

Numerical solution for a class of fractional optimal control problems using the fractional-order Bernoulli functions

Abstract: The main purpose of this paper is to provide an efficient method for solving some types of fractional optimal control problems governed by integro-differential and differential equations, and because finding the analytical solutions to these problems is usually difficult, a numerical method is proposed. In this study, the fractional-order Bernoulli functions (F-BFs) are applied as basis functions and a new operational matrix of fractional integration is constructed for these functions. In the first step, the p… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2

Citation Types

0
2
0

Year Published

2023
2023
2023
2023

Publication Types

Select...
3

Relationship

0
3

Authors

Journals

citations
Cited by 3 publications
(2 citation statements)
references
References 53 publications
0
2
0
Order By: Relevance
“…However, it is usually difficult to solve optimal control problems analytically for complex nonlinear dynamic systems, especially when the state-space region and control inputs are bounded (Fard et al, 2019). Some effective numerical methods (Valian et al, 2022; Wei and Liu, 2014) to solve optimal control problems for complex nonlinear systems have been studied. The cell mapping was proposed (Hsu, 1985) as an effective numerical method to obtain global optimal control solutions for nonlinear dynamical systems.…”
Section: Introductionmentioning
confidence: 99%
“…However, it is usually difficult to solve optimal control problems analytically for complex nonlinear dynamic systems, especially when the state-space region and control inputs are bounded (Fard et al, 2019). Some effective numerical methods (Valian et al, 2022; Wei and Liu, 2014) to solve optimal control problems for complex nonlinear systems have been studied. The cell mapping was proposed (Hsu, 1985) as an effective numerical method to obtain global optimal control solutions for nonlinear dynamical systems.…”
Section: Introductionmentioning
confidence: 99%
“…However, many phenomena of real life may display memory and genetic characteristics that cannot be modeled by an integer-order PDE-ODE system. Fractional-order calculus has been confirmed to be an effective instrument for many practical scientific engineering models (Valian et al, 2021; Zhou, 2016). In real problems, fractional differential equations are superior to traditional integer-order equations in describing all kinds of materials with memory properties (Jahanshahi et al, 2021), genetic (Ushakov et al, 2020), and simulating dynamic processes (such as fractal media).…”
Section: Introductionmentioning
confidence: 99%