基于分数随机脉冲系统的汉密尔顿-雅各比-贝尔曼方程

Yu Guo, Zhenyi Dai
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The lack of semi group properties in fractional order makes the original dynamic programming methods unable to directly handle fractional order problems. We have dealt with this problem by combining the properties of fractional order integrals. In solving this problem, we found that the order of the original system in HJB equation is at least 1. 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引用次数: 0

摘要

在本讲座中,我们考虑了分数阶随机脉冲微分方程(1<β<2$$ 1<\beta <2$$)的最优控制问题,现有文献中还没有针对分数阶微分方程提出相应的汉密尔顿-贾可比-贝尔曼(HJB)方程。分数阶微分方程缺乏半群性质,使得原有的动态编程方法无法直接处理分数阶问题。我们结合分数阶积分的特性处理了这一问题。在解决这个问题时,我们发现 HJB 方程中原系统的阶数至少为 1。当阶数小于 1 时,我们的分数阶思想方法为解决问题提供了可能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Hamilton-Jacobi-Bellman equation based on fractional random impulses system

Hamilton-Jacobi-Bellman equation based on fractional random impulses system
In this talk, we consider the optimal control problem for fractional order random impulses differential equations (), and there is no corresponding Hamilton-Jacobi-Bellman (HJB) equation proposed for fractional order differential equations in existing literature. The lack of semi group properties in fractional order makes the original dynamic programming methods unable to directly handle fractional order problems. We have dealt with this problem by combining the properties of fractional order integrals. In solving this problem, we found that the order of the original system in HJB equation is at least 1. When the order is less than 1, our approach to fractional order ideas provides a possibility to solve the problem.
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