论分数阶系统优化控制问题中庞特里亚金最大原则与汉密尔顿-雅各比-贝尔曼方程之间的关系

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2023-12-29 DOI:10.1134/s0012266123011006x

M. I. Gomoyunov

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引用次数: 0

摘要

摘要我们考虑了一个最优控制问题，即如何使一个运动由带有卡普托分数导数的微分方程描述的动力系统的终端成本函数最小化。我们研究了庞特里亚金最大原则形式的必要最优条件与带有所谓分数共变导数的汉密尔顿-雅各比-贝尔曼方程之间的关系。研究证明，庞特里亚金最大原理中的代价变量与沿最优运动计算的最优结果函数的分数共变梯度在符号上是重合的。

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On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems

Abstract

We consider the optimal control problem of minimizing the terminal cost functional for a dynamical system whose motion is described by a differential equation with Caputo fractional derivative. The relationship between the necessary optimality condition in the form of Pontryagin’s maximum principle and the Hamilton–Jacobi–Bellman equation with so-called fractional coinvariant derivatives is studied. It is proved that the costate variable in the Pontryagin maximum principle coincides, up to sign, with the fractional coinvariant gradient of the optimal result functional calculated along the optimal motion.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.