带噪声记忆的非零和随机微分博弈问题的充分最大值原理

doi:10.6040/j.issn.1671-9352.0.2023.281

摘要/Abstract

摘要： 研究一类非零和随机微分博弈问题,其主要特点是状态变量和控制变量可以带有多种形式的时滞。状态变量可以带有分布时滞、离散时滞与噪声记忆,控制变量可以带有分布时滞与离散时滞。控制域为凸集。利用最大值原理方法建立该博弈问题的均衡点所满足的充分条件。最后研究一个例子,给出均衡点的显式表达式。

关键词: 非零和随机微分博弈, 时滞, 噪声记忆, 均衡点, 最大值原理

Abstract: One nonzero-sum stochastic differential game is considered, whose main feature is that several kinds of delays of the state and the control are involved. The state process can contain distributed delays, discrete delays, and noisy memory, and control processes can contain distributed delays and discrete delays. The control domains are convex sets. Sufficient conditions for the equilibrium point of the game are established by means of the stochastic maximum principle. Finally, an illustrative example is considered for which the equilibrium point is obtained in explicit form.

Key words: nonzero-sum stochastic differential game, delay, noisy memory, equilibrium point, maximum principle

中图分类号:

O232

张峰,梁嘉玮. 带噪声记忆的非零和随机微分博弈问题的充分最大值原理[J]. 《山东大学学报(理学版)》, 2024, 59(10): 46-52.

ZHANG Feng, LIANG Jiawei. Sufficient maximum principle for one kind of nonzero-sum stochastic differential game involving noisy memory[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 46-52.

参考文献

[1] YONG Jiongmin, ZHOU Xunyu. Stochastic controls: Hamiltonian systems and HJB equations[M]. New York: Springer, 1999:101-156.
[2] PENG Shige, YANG Zhe. Anticipated backward stochastic differential equations[J]. The Annals of Probability, 2009, 37(3):877-902.
[3] CHEN Li, WU Zhen. Maximum principle for the stochastic optimal control problem with delay and application[J]. Automatica, 2010, 46(6):1074-1080.
[4] MENG Weijun, SHI Jingtao. A global maximum principle for stochastic optimal control problems with delay and applications[J]. Systems & Control Letters, 2021, 150:104909.
[5] KSENDAL B, SULEM A, ZHANG T S. Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations[J]. Advances in Applied Probability, 2011, 43(2):572-596.
[6] CHEN Li, WU Zhen. Stochastic optimal control problem in advertising model with delay[J]. Journal of Systems Science & Complexity, 2020, 33(4):968-987.
[7] ZHANG Feng. Stochastic maximum principle for optimal control problems involving delayed systems[J]. Science China Information Sciences, 2021, 64(1):119206.
[8] ZHANG Feng. Stochastic maximum principle of mean-field jump-diffusion systems with mixed delays[J]. Systems & Control Letters, 2021, 149:104874.
[9] ZHANG Qixia. Maximum principle for stochastic optimal control problem with distributed delays[J]. Acta Mathematica Scientia, 2021, 41(2):437-449.
[10] MENG Weijun, SHI Jingtao, WANG Tianxiao, et al. A general maximum principle for optimal control of stochastic differential delay systems[EB/OL].(2023-02-07)[2023-06-27]. https://arxiv.org/abs/2302.03339.
[11] DAHL K, MOHAMMED S E A, KSENDAL B, et al. Optimal control of systems with noisy memory and BSDEs with Malliavin derivatives[J]. Journal of Functional Analysis, 2016, 271(2):289-329.
[12] ZHANG Feng. Sufficient maximum principle for stochastic optimal control problems with general delays[J]. Journal of Optimization Theory and Applications, 2022, 192(2):678-701.
[13] ZHANG Qixia. Maximum principle for non-zero sum stochastic differential game with discrete and distributed delays[J]. Journal of Systems Science & Complexity, 2021, 34(2):572-587.

相关文章 15

[1]	王晓,刘重阳,胡电中,刘刚. 1,3-丙二醇间歇发酵中的时滞最优控制[J]. 《山东大学学报(理学版)》, 2024, 59(1): 124-131, 138.
[2]	王雅迪,袁海龙. 时滞Lengyel-Epstein反应扩散系统的Hopf分支[J]. 《山东大学学报(理学版)》, 2023, 58(8): 92-103.
[3]	孙盼,张旭萍. 具有无穷时滞脉冲发展方程解的连续依赖性[J]. 《山东大学学报(理学版)》, 2023, 58(6): 77-83, 91.
[4]	许越,韩晓玲. 具有双时滞的媒体效应对西藏地区包虫病控制的影响[J]. 《山东大学学报(理学版)》, 2023, 58(5): 53-62.
[5]	郭改慧,王晶晶,李旺瑞. 一类具有时滞的植被-水反应扩散模型的Hopf分支[J]. 《山东大学学报(理学版)》, 2023, 58(10): 32-42, 53.
[6]	李永花,张存华. 具有Dirichlet边界条件的单种群时滞反应扩散模型的稳定性[J]. 《山东大学学报(理学版)》, 2023, 58(10): 122-126.
[7]	李蕾,叶永升. 具有Dirichlet有界条件的反应扩散Cohen-Grossberg神经网络指数稳定性[J]. 《山东大学学报(理学版)》, 2023, 58(10): 67-74.
[8]	庞玉婷,赵东霞,鲍芳霞. 具有多时滞和多参数的双向环状网络的稳定性[J]. 《山东大学学报(理学版)》, 2022, 57(8): 103-110.
[9]	王苗苗,丁小丽,李佳敏. 分数阶随机时滞微分方程的波形松弛方法[J]. 《山东大学学报(理学版)》, 2022, 57(1): 101-110.
[10]	沈维,张存华. 时滞食饵-捕食系统的多次稳定性切换和Hopf分支[J]. 《山东大学学报(理学版)》, 2022, 57(1): 42-49.
[11]	魏立祥,张建刚,南梦冉,张美娇. 具有时滞的磁通神经元模型的稳定性及Hopf分岔[J]. 《山东大学学报(理学版)》, 2021, 56(5): 12-22.
[12]	马维凤,陈鹏玉. 状态依赖型时滞微分方程的解流形及其C¹-光滑性[J]. 《山东大学学报(理学版)》, 2021, 56(2): 92-96.
[13]	吴臻,王光臣,李敏. 正倒向随机最优控制问题的最大值原理:完全信息和部分信息[J]. 《山东大学学报(理学版)》, 2021, 56(10): 1-10.
[14]	马德青,胡劲松. 消费者参考质量存在时滞效应的动态质量改进策略[J]. 《山东大学学报(理学版)》, 2020, 55(9): 101-89.
[15]	章欢,李永祥. 含时滞导数项的高阶常微分方程的正周期解[J]. 《山东大学学报(理学版)》, 2019, 54(4): 29-36.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed