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 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields 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

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.