分数阶系统线性二次最优控制问题中的值泛函与最优反馈控制

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-08-30 DOI:10.3934/mcrf.2023002

M. Gomoyunov

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引用次数: 2

摘要

研究了一类用线性卡普托分数阶微分方程和二次代价泛函描述的动力系统的有限视界最优控制问题。给出了值泛函的显式公式，其中包含了某Fredholm积分方程的解。提出了一种用于构造任意精度$\varepsilon>0$的$\varepsilon$最优控制器的分步反馈控制方法。获得这些结果的基础是研究具有所谓分数阶协变导数的相关Hamilton-Jacobi-Bellman方程的解。

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Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system

In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional is given, which includes a solution of a certain Fredholm integral equation. A step-by-step feedback control procedure for constructing $\varepsilon$-optimal controls with any accuracy $\varepsilon>0$ is proposed. The basis for obtaining these results is the study of a solution of the associated Hamilton-Jacobi-Bellman equation with so-called fractional coinvariant derivatives.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.