论文标题
分数订单系统线性 - 季度最佳控制问题中的价值功能和最佳反馈控制
Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system
论文作者
论文摘要
在本文中，考虑了一个有限的摩尼子最佳控制问题，该问题涉及由线性caputo分数微分方程和二次成本函数描述的动力系统。给出了值函数的明确公式，其中包括某个弗雷德姆积分方程的解决方案。提出了用于构建$ \ varepsilon $ - 最佳控件的分步反馈控制步骤，并提出了任何精度$ \ varepsilon> 0 $。获得这些结果的基础是研究与所谓的分数共依因衍生物的相关汉密尔顿 - 雅各比 - 贝尔曼方程的解决方案。
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.
