具有混合延迟和噪声观测的最优控制问题的随机最大原则

IF 2.5 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

European Journal of Control Pub Date : 2024-07-02 DOI:10.1016/j.ejcon.2024.101073

Heping Ma , Yu Shi

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引用次数: 0

摘要

本文研究了有延迟的随机微分方程所控制的状态的最优控制问题，以及部分由噪声过程观测到的状态的最优控制问题。建立了一些变分不等式和最优的必要条件。同时，我们引入了两种邻接方程，并证明它们是等价的。作为应用，我们提出了一个线性二次系统和一个金融问题来证明我们的结果。特别是，我们用数值模拟和一些数字来说明延迟对最优解的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Stochastic maximum principle for optimal control problems with mixed delays and noisy observations

In this paper, we study the optimal control problem for the state governed by stochastic differential equation with delay and partially observed by a noisy process. Some variational inequalities and a necessary condition for optimality are established. Meanwhile, we introduce two kinds of adjoint equation which are shown to be equivalent. As an application, a linear–quadratic system and a financial problem are presented to demonstrate our results. In particular, its numerical simulation and some figures are used to illustrate the effect of delay on optimal solutions.

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来源期刊

European Journal of Control 工程技术-自动化与控制系统

CiteScore

5.80

自引率

5.90%

发文量

131

审稿时长

1 months

期刊介绍： The European Control Association (EUCA) has among its objectives to promote the development of the discipline. Apart from the European Control Conferences, the European Journal of Control is the Association''s main channel for the dissemination of important contributions in the field. The aim of the Journal is to publish high quality papers on the theory and practice of control and systems engineering. The scope of the Journal will be wide and cover all aspects of the discipline including methodologies, techniques and applications. Research in control and systems engineering is necessary to develop new concepts and tools which enhance our understanding and improve our ability to design and implement high performance control systems. Submitted papers should stress the practical motivations and relevance of their results. The design and implementation of a successful control system requires the use of a range of techniques: Modelling Robustness Analysis Identification Optimization Control Law Design Numerical analysis Fault Detection, and so on.