A linear quadratic stochastic Stackelberg differential game with time delay

IF 0.9 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2020-12-28 DOI:10.3934/mcrf.2021035

Weijun Meng, Jingtao Shi

引用次数: 6

Abstract

. This paper is concerned with a linear quadratic stochastic Stackelberg diﬀerential game with time delay. The model is general, in which the state delay and the control delay both appear in the state equation, moreover, they both enter into the diﬀusion term. By introducing two Pseudo-Riccati equations and a special matrix equation, the state feedback representation of the open-loop Stackelberg strategy is derived, under some assumptions. Fi- nally, two examples are given to illustrate the applications of the theoretical results.

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具有时滞的线性二次随机Stackelberg微分对策

．研究一类具有时滞的线性二次随机Stackelberg微分对策。该模型具有通用性，状态时滞和控制时滞都出现在状态方程中，并且都进入扩散项。通过引入两个伪riccati方程和一个特殊矩阵方程，在一定的假设条件下，导出了开环Stackelberg策略的状态反馈表示。最后，给出了两个实例来说明理论结果的应用。

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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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.