用于数值求解延迟相关分数最优控制问题的精确有限差分公式

D. Băleanu, M. Hajipour, A. Jajarmi
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引用次数: 0

摘要

时延分数最优控制问题(OCPs)是一个重要的研究领域,用于开发有效的控制和优化策略,以解决物理学、化学、生物学和工程学等各种自然科学中出现的复杂现象。通过考虑带有时间延迟的分数 OCP,我们可以设计出考虑到系统历史的控制策略,并优化其在给定时间范围内的行为。然而,应用庞特里亚金(Pontryagin)最大化原理来解决这些问题会导致边界值问题(BVP),其中包括延迟和提前项,从而使分析求解变得困难和苛刻。为解决这一问题,本文提出了一种精确的有限差分公式,用于数值求解上述提前-延迟 BVP。本文提供了所建议近似方法的误差分析和收敛特性,并通过几个示例证明了所建议方法的适用性、有效性和准确性。仿真结果证实了所提技术在延迟分式动力方程优化控制方面的优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An accurate finite difference formula for the numerical solution of delay-dependent fractional optimal control problems
Time-delay fractional optimal control problems (OCPs) are an important research area for developing effective control and optimization strategies to address complex phenomena occurring in various natural sciences, such as physics, chemistry, biology, and engineering. By considering fractional OCPs with time delays, we can design control strategies that take into account the system's history and optimize its behavior over a given time horizon. However, applying the Pontryagin principle of maximization to solve these problems leads to a boundary value problem (BVP) that includes delay and advance terms, making analytical solutions difficult and demanding. To address this issue, this paper presents a precise finite difference formula to solve the aforementioned advance-delay BVP numerically. The suggested approximate method's error analysis and convergence properties are provided, and several illustrative examples demonstrate the applicability, validity, and accuracy of the proposed approach. Simulation results confirm the proposed technique's advantages for the optimal control of delay fractional dynamical equations.
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