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具有随机脉冲的布尔控制网络的集合稳定性研究

胡鑫1,黄迟2   

  1. 1. 太原理工大学数学学院,太原 030024; 2. 西南财经大学经济信息工程学院, 成都 611130
  • 出版日期:2020-04-25 发布日期:2020-05-30

胡鑫,黄迟. 具有随机脉冲的布尔控制网络的集合稳定性研究[J]. 系统科学与数学, 2020, 40(4): 587-598.

HU Xin1, HUANG Chi. Set Stabilization of Boolean Control Networks with Stochastic Impulse[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(4): 587-598.

Set Stabilization of Boolean Control Networks with Stochastic Impulse

HU Xin1, HUANG Chi2   

  1. 1. College of Mathematics, Taiyuan University of Technology, Taiyuan 030024; 2. School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu 611130
  • Online:2020-04-25 Published:2020-05-30

在文章研究的具有随机脉冲的布尔控制网络的集合稳定性 问题中, 随机脉冲的引入使得模型对实际问题的研究更具真实性. 首先, 随机脉冲被描述为一组可供选择的具有相应概率的常规模型集合. 同时, 文章 明确集合稳定性问题的目的是将系统中所有节点以概率1到达并稳定到给定 节点集合. 其次, 提出一个判断给定系统的集合稳定性的充要条件. 然 后, 对于可集合稳定系统, 给出控制器和脉冲策略的设计方法. 最后, 通过一个数例说明获得成果的有效性.

In this paper, we analyze the set stabilization problem of Boolean control networks with stochastic impulse. The introduction of stochastic impulse model makes the study more realistic. First, stochastic impulse are described as a series of possible models with corresponding probabilities. And the definition of set stabilization problem, which is to make all states in the system reach and stabilize to a given set with probability 1, is given. Second, a necessary and sufficient condition is presented to judge whether a given system is set stable. Then, for the set stable system, system controller and states impulse strategies design methods are proposed. Finally, the effectiveness of the obtained results is demonstrated by an example.

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