单比特函数摄动下干扰布尔网络输出调节问题的可解性  

The Solvability of Output Regulation Problem forBoolean Networks with Disturbance Inputs underOne-Bit Function Perturbation

作　　者：曹秀君 付世华[1] 赵建立[1] 李新岭 CAO Xiujun;FU Shihua;ZHAO Jianli;LI Xinling(School of Mathematics Science,Liaocheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《聊城大学学报(自然科学版)》2025年第2期159-169,共11页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(62103176);山东省自然科学基金项目(ZR2022MA030)资助。

摘　　要：研究干扰布尔网络在单比特函数摄动下的输出调节问题。首先,利用矩阵半张量积,分别确立了带干扰的布尔网络以及参考系统的代数形式。其次,通过建立一个增广系统,将输出调节问题转化为增广系统的鲁棒集合稳定性问题。并且,通过构造一系列状态集合,得到了干扰布尔网络的输出在函数摄动之后仍然可以追踪上参考系统输出的几个判断准则。最后,给出一个例子验证本文所得结果的有效性。This article investigates the output regulation problem of Boolean networks with disturbance inputs under one-bit function perturbation.First,with the help of the semi-tensor product of matrices,the algebraic forms of Boolean networks with disturbances and the reference system are established,respectively.Then,by constructing an augmented system,the output regulation problem is transformed into the robust set stability problem of the augmented system.Moreover,by constructing a sequence of state sets,several criteria are obtained to verify whether the output of the Boolean networks with disturbances can still track the output of the reference system after function perturbation.Finally,an example is given to verify the effectiveness of the results obtained in this paper.

关 键 词：布尔网络 输出调节 干扰输入 单比特函数摄动 矩阵半张量积 

分 类 号：O157.5[理学—数学] O231[理学—基础数学]