On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems
Pub Date : 2023-12-29
DOI:10.1134/s0012266123011006x
引用次数: 0
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.
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
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。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
求助全文
约1分钟内获得全文
求助全文
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
