解决分数最优控制问题的新方法

IF 2.3 3区 工程技术 Q2 ACOUSTICS Journal of Vibration and Control Pub Date : 2024-07-22 DOI:10.1177/10775463241264329
Sondos M Syam, Z Siri, Sami H Altoum, R Md Kasmani
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引用次数: 0

摘要

在本文中,我们提出了一种利用运算矩阵法解决分数最优控制问题的新方法。我们结合线性射击法,解决了共态函数初始条件缺失的难题。我们的目标是提供一种不仅能提高计算效率、降低成本,还能提高准确性和可用性的方法。利用我们的新方法,我们可以计算扩展解的系数,而无需求解代数系统。这些系数可以显式生成,也可以通过迭代过程生成。我们证明了近似函数序列对最优控制问题唯一解的均匀收敛性。为了证明我们提出的方法的有效性,我们解决了几个数值示例,并将结果与其他研究人员获得的结果进行了比较。此外,我们还将这种新方法的应用扩展到解决多状态问题,从而将其应用范围扩展到更广泛的问题领域。这样,我们就能用同样高效、准确的方法来解决不同的问题。通过我们的研究,我们为开发解决分数最优控制问题的功能强大、用途广泛的方法做出了贡献,与现有技术相比具有显著优势。
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A new method for solving fractional optimal control problems
In this article, we present a novel approach that utilizes the operational matrix method to solve fractional optimal control problems. We address the challenge of missing initial conditions for the co-state function by incorporating the linear shooting method. Our objective is to provide a method that not only enhances computational efficiency and reduces cost but also improves accuracy and usability. With our new approach, we can calculate the coefficients of the expansion solution without the need to solve an algebraic system. These coefficients can be generated explicitly or through an iterative process. We provide a proof of the uniform convergence of the approximate series of functions to the unique solution of the optimal control problem. To demonstrate the effectiveness of our proposed method, we solve several numerical examples and compare the results with those obtained by other researchers. Additionally, we extend the application of this new method to solve problems with multiple states, thereby expanding its scope to a wider range of problem domains. This allows us to address diverse scenarios using the same efficient and accurate approach. Through our research, we contribute to the development of a powerful and versatile method for solving fractional optimal control problems, offering significant advantages over existing techniques.
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来源期刊
Journal of Vibration and Control
Journal of Vibration and Control 工程技术-工程:机械
CiteScore
5.20
自引率
17.90%
发文量
336
审稿时长
6 months
期刊介绍: The Journal of Vibration and Control is a peer-reviewed journal of analytical, computational and experimental studies of vibration phenomena and their control. The scope encompasses all linear and nonlinear vibration phenomena and covers topics such as: vibration and control of structures and machinery, signal analysis, aeroelasticity, neural networks, structural control and acoustics, noise and noise control, waves in solids and fluids and shock waves.
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