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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 29-36.doi: 10.6040/j.issn.1671-9352.0.2015.271

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一类非线性脉冲微分系统爆炸解的随机压制

张春艳1,郝胜男1*,冯立超2   

  1. 1. 华北理工大学信息工程学院, 河北 唐山 063009;2. 华北理工大学理学院, 河北 唐山 063009
  • 收稿日期:2015-06-08 出版日期:2016-02-16 发布日期:2016-03-11
  • 通讯作者: 郝胜男(1971— ),女,副教授,主要从事随机控制、鲁棒控制的研究.E-mail:hshengnan@126.com E-mail:zhang-chunyan3061@163.com
  • 作者简介:张春艳(1982— ),女,硕士,主要从事随机控制、鲁棒控制的研究.E-mail:zhang-chunyan3061@163.com
  • 基金资助:
    河北省青年基金项目(A2014209240);唐山市科技计划项目(13130214z);华北理工大学研究生项目(K1407)

Stochastic suppression on explosive solutions of a class of nonlinear impulsive differential systems by noise

ZHANG Chun-yan1, HAO Sheng-nan1*, FENG Li-chao2   

  1. 1. College of Information Engineering, North China University of Science and Technology, Tangshan 063009, Hebei, China;
    2. College of Science, North China University of Science and Technology, Tangshan 063009, Hebei, China
  • Received:2015-06-08 Online:2016-02-16 Published:2016-03-11

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摘要： 主要探讨了随机噪音对非线性脉冲微分系统爆炸解的随机压制问题。对一个给定的非线性脉冲微分系统,当满足单边多项式增长条件时很可能在有限时间内出现爆炸解;引入一个多项式随机噪音σ|x(t)|βx(t)dB(t)(其中B(t)为Brownian运动)来压制非线性脉冲微分系统的潜在爆炸解,使其对应的随机摄动脉冲微分系统存在唯一的全局解,且该全局解矩有界,随机一致有界,最多以多项式形式增长。

关键词: 爆炸解, Itó公式, 单边多项式增长条件, 脉冲微分系统, 随机噪音

Abstract: We investigate the problem of stochastic suppression on explosive solutions of nonlinear impulsive differential systems by noise. For a given nonlinear impulsive differential system satisfying one-sided polynomial growth condition which may explode at a finite time, we introduce a polynomial stochastic noise σ|x(t)|βx(t)dB(t)(B(t)is a Brownian motion)such that there exists a unique global solution for the corresponding stochastically perturbed impulsive differential system. The global solution is bounded in the sense of the moment and the trajectory with large probability and the global solution grow at most polynomial.

Key words: one-sided polynomial growth condition, impulsive differential systems, Itó formula, stochastic noise, explosive solutions

中图分类号: 

  • O231.3
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