具概率延迟反馈金融系统的脉冲控制

阿子阿英; 饶若峰; 赵锋; 黄鸿燕; 王雪; 刘浩

doi:10.21656/1000-0887.400059

具概率延迟反馈金融系统的脉冲控制

doi: 10.21656/1000-0887.400059

¹成都师范学院数学学院, 成都 611130;²成都师范学院金融数字研究所, 成都 611130

详细信息

作者简介:
阿子阿英(1997—),女,彝族(E-mail: ruopheng@hotmail.com);饶若峰(1969—),男,教授(通讯作者. E-mail: ruofengrao@163.com);赵锋(1995—),男(E-mail: rrf2@163.com);黄鸿燕(1997—),女(E-mail: rrf2003@163.com);王雪（1998—），女(E-mail: 2637214132@qq.com);刘浩（1996—），男(E-mail: 1278891455@qq.com).

中图分类号: O175.13
计量
- 文章访问数: 1130
- HTML全文浏览量: 225
- PDF下载量: 301
- 被引次数: 0
出版历程
- 收稿日期: 2019-02-25
- 修回日期: 2019-02-28
- 刊出日期: 2019-12-01

Impulse Control of Financial Systems With Probabilistic Delay Feedback

¹Department of Mathematics, Chengdu Normal University, Chengdu 611130, P.R.China;²Institute of Financial Mathematics, Chengdu Normal University, Chengdu 611130, P.R.China

摘要

摘要: 研究了概率时滞脉冲金融系统平衡点的全局渐近稳定性问题。首先，通过定义合适的时滞分段区间上的随机变量，给出了概率时滞的脉冲金融系统的数学模型，根据脉冲微分不等式特点构造了一个简便合适的Lyapunov函数利用脉冲微分不等式引理、控制脉冲间隔与脉冲量以及概率时滞分析技巧,获得了较大时滞允许范畴下的平衡点的全局指数稳定,并通过数值实例验证了方法的可行性以及概率时滞的优势。特别地,稳定性判定准则的时滞允许上限的增大,扩大了准则的实用性.
- 概率时滞 /
- 脉冲微分不等式 /
- Lyapunov函数 /
- MATLAB LMI工具箱
Abstract: The global asymptotic stability of equilibrium points of impulsive financial systems with probabilistic delays was studied. Firstly, through definition of the random variables on the appropriate time-delay intervals, the mathematical model for the impulsive financial system with probabilistic time delay was given. According to the characteristics of impulsive differential inequalities, a simple and suitable Lyapunov function was constructed. By means of the impulsive differential inequality lemma, the technique of controlling impulse interval & impulse quantity and the probabilistic time delay analysis, the global exponential stability of the equilibrium point in the permissible category of large delays was obtained. Finally, the feasibility of the proposed method and the advantages of probabilistic delay were verified with a numerical example. In particular, the increase of the time delay allowable upper limit to the stability criterion enlarges the practicability of the criterion.
- probabilistic delay /
- impulsive differential inequality /
- Lyapunov function /
- MATLAB LMI toolbox

HTML全文

参考文献(17)

[1]	马军海, 陈予恕. 一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究[J]. 应用数学和力学, 2001,22(11): 1119-1128.(MA Junhai, CHEN Yushu. Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system[J]. Applied Mathematics and Mechanics,2001,22(11): 1119-1128.(in Chinese))
[2]	马军海, 陈予恕. 一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究[J]. 应用数学和力学, 2001,22(12): 1236-1242.(MA Junhai, CHEN Yushu. Study for the bifurcation topological structure and the global complicated character of a kind of non-linear finance system[J]. Applied Mathematics and Mechanics,2001,22(12): 1236-1242.(in Chinese))
[3]	ZHANG R Y. Bifurcation analysis for a kind of nonlinear finance system with delayed feedback and its application to control of chaos[J]. Journal of Applied Mathematics,2012,2012: 316390.
[4]	PYRAGAS K. Continuous control of chaos by self-controlling feedback[J]. Physics Letters A,1992,170(6): 421-429.
[5]	CHEN W C. Dynamics and control of a financial system with time-delayed feedbacks[J]. Chaos, Solitons & Fractals,2008,37(4): 1198-1207.
[6]	姚洪兴, 潘虹, 齐丽丽. 一类含脉冲延迟反馈金融系统的稳定性分析[J]. 江苏大学学报(自然科学版), 2011,〖STHZ〗 32(2): 241-244.(YAO Hongxing, PAN Hong, QI Lili. Global exponential stability of a financial system with impulses and time-delayed feedbacks[J]. Journal of Jiangsu University(Science Edition),2011,32(2): 241-244.(in Chinese))
[7]	RAO R F, ZHONG S M, WANG X R. Delay-dependent exponential stability for Markovian jumping stochastic Cohen-Grossberg neural networks with p -Laplace diffusion and partially known transition rates via a differential inequality[J]. Advances in Difference Equations,2013,2013: 183.
[8]	SONG Q K, YAN H, ZHAO Z J, et al. Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays[J]. Neural Networks,2016,81: 1-10.
[9]	WANG L M, SONG Q K, LIU Y R, et al. Global asymptotic stability of impulsive fractional-order complex-valued neural networks with time delay[J]. Neurocomputing,2017,243: 49-59.
[10]	岳东, 许世范, 刘永清. 脉冲时滞微分不等式及鲁棒控制设计中的应用[J]. 控制理论与应用, 1999,16(4): 519-524.(YUE Dong, XU Shifan, LIU Yongqing. Differential inequality with delay and impulse and its applications to design robust control[J]. Control Theory Applications,1999,16(4): 519-524.(in Chinese))
[11]	张磊, 宋乾坤. 带有比例时滞的复值神经网络全局指数稳定性[J]. 应用数学和力学, 2018,39(5): 584-591.(ZHANG Lei, SONG Qiankun. Global exponential stability of complex-valued neural networks with proportional delays[J]. Applied Mathematics and Mechanics,2018,39(5): 584-591.(in Chinese))
[12]	舒含奇, 宋乾坤. 带有时滞的Clifford值神经网络的全局指数稳定性[J]. 应用数学和力学, 2017,38(5): 513-525.(SHU Hanqi, SONG Qiankun. Global stability of Clifford-valued recurrent neural networks with mixed time-varying delays[J]. Applied Mathematics and Mechanics,2017,38(5): 513-525.(in Chinese))
[13]	ZHANG X H, WU S L, LI K L. Delay-dependent exponential stability for impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms[J]. Communications in Nonlinear Science and Numerical Simulation,2011,16(3): 1524-1532.
[14]	黎克麟, 曾意. 具有多滞后的区间非线性Lurie控制系统的鲁棒绝对稳定性[J]. 四川师范大学学报(自然科学版), 2007,30(1): 27-30.(LI Kelin, ZENG Yi. Robust absolute stability of interval nonlinear Lurie control systems with multi-delay[J]. Journal of Sichuan Normal University（Natural Scicence）,2007,30(1): 27-30.(in Chinese))
[15]	LI K L, ZHANG X H, LI Z A. Global exponential stability of impulsive cellular neural networks with time-varying and distributed delay[J]. Chaos, Solitons & Fractals,2009,41(3): 1427-1434.
[16]	曾德强, 吴开腾, 宋乾坤, 等. 时滞神经网络随机抽样控制的状态估计[J]. 应用数学和力学, 2018,39(7): 821-832.(ZENG Deqiang, WU Kaiteng, SONG Qiankun, et al. State estimation for delayed neural networks with stochastic sampled-data control[J]. Applied Mathematics and Mechanics,2018,39(7): 821-832.(in Chinese))
[17]	RAO Ruofeng. Global stability of a Markovian jumping chaotic financial system with partially unknown transition rates under impulsive control involved in the positive interest rate[J]. Mathematics,2019,7(7): 579.