k-值控制网络的可控性与可观性

doi:10.6040/j.issn.1671-9352.0.2014.162

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (04): 27-35.doi: 10.6040/j.issn.1671-9352.0.2014.162

k-值控制网络的可控性与可观性

邓磊, 赵建立, 刘华, 李莹

聊城大学数学科学学院, 山东聊城 252000

收稿日期:2014-04-16 修回日期:2014-11-07 出版日期:2015-04-20 发布日期:2015-04-17
通讯作者: 赵建立(1964-),男,教授,研究方向为数值计算及应用.E-mail:zhaojl1964@126.com E-mail:zhaojl1964@126.com
作者简介:邓磊(1984-),男,硕士研究生,研究方向为矩阵理论及其应用.E-mail:dengleiliaoda@163.com
基金资助:
国家自然科学基金资助项目(11171226);国家自然科学基金资助项目(11301247);山东省自然科学基金资助项目(ZR2012FQ005)

Controllability and observability of k-valued control networks

DENG Lei, ZHAO Jian-li, LIU Hua, LI Ying

School of Mathmatics Science, Liaocheng University, Liaocheng 252000, Shandong, China

Received:2014-04-16 Revised:2014-11-07 Online:2015-04-20 Published:2015-04-17

摘要/Abstract

摘要： 利用矩阵的半张量积,研究了k-值控制网络的可控性与可观性问题.通过特征函数构造出可控性矩阵,得到了新的可控性充分和必要条件,简化了原有条件的计算复杂性,矩阵的最高阶数由原来的k^n+m 降到kⁿ.另外,还得到了检验k-值控制网络可观性的条件,该条件更容易计算检验.

关键词: 可观性, 特征函数, 半张量积, k-值控制网络, 可控性

Abstract: By using the method of semi-tensor product of matrices, the controllability and observability of k-valued control networks were investigated. Controllability matrix was constructed by eigenfunction and a novel necessary and sufficient condition for controllability was given. The new conditions simplify computational complexity of original conditions,and the highest power of matrix is reduced from k^n+m to kⁿ. Aslo, a sufficient condition for observabilitywas obtained, which can be computed easily.

Key words: k-valued control network, eigenfunction, semi-tensor product of matrices, observability, controllability

中图分类号:

O233

邓磊, 赵建立, 刘华, 李莹. k-值控制网络的可控性与可观性[J]. 山东大学学报（理学版）, 2015, 50(04): 27-35.

DENG Lei, ZHAO Jian-li, LIU Hua, LI Ying. Controllability and observability of k-valued control networks[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 27-35.

参考文献

[1] KAUFFMAN A S. Metabolic stability and epigenesis in randomly constructed genetic nets[J]. Theoretical Biology, 1969, 22(3):437-467.
[2] CHENG Daizhan, QI Hongsheng. Input-state approach to Boolean networks[J]. IEEE Transactions on Neuralnetworks, 2009, 20(3):512-521.
[3] CHENG Daizhan, QI Hongsheng, LI Zhiqiang. Identification of Boolean control networks[M]//Analysis and Control of Boolean Networks. London:Springer, 2011:389-407.
[4] CHENG Daizhan, QI Hongsheng, LI Zhiqiang. Controllability and observability of Boolean control networks[M]//Analysis and Control of Boolean Networks. London: Springer, 2011:213-231.
[5] ZHAO Yin, CHENG Daizhan. On controllability and stabilizability of probabilistic Boolean control networks[J]. Science China Information Sciences, 2014, 57(1):1-14.
[6] CHENG Daizhan, QI Hongsheng, LI Zhiqiang, et al. Stability and stabilization of Boolean networks[J]. International Journal of Robust and Nonlinear Control, 2011, 21(2): 134-156.
[7] 程代展, 齐洪胜, 赵寅. 布尔网络的分析与控制—矩阵半张量积方法[J]. 自动化学报, 2011, 37(5):529-540. CHENG Daizhan, QI Hongsheng, ZHAO Yin. Analysis and control of Boolean networks: a Semi-tensor product approach[J]. Acta Automatica Sinica, 2011, 37(5):529-540.
[8] CHENG Daizhan. Semi-tensor product of matrices and its application to Margan's problems[J]. Science in China, 2001, 44(3):195-212.
[9] LI Fangfei, SUN Jitao. Stability and stabilization of multivalued logical networks[J]. Nonlinear Analysis: Real World Applications, 2011, 12(6):3701-3712.
[10] LI Haitao, WANG Yuzhen, LIU Zhenbin. Existence and number of fixed points of Boolean transformations via the semi-tensor product method[J]. Applied Mathematics Letters, 2012, 25(8):1142-1147.
[11] 潘金凤, 赵建立, 付世华. 逻辑切换控制网络的可控性和稳定性[J]. 山东大学学报:工学版, 2013, 43(4):62-67. PAN Jinfeng, ZHAO Jianli, FU Shihua. On constrollability and stability of switched logical control networks[J]. Journal of Shandong University, 2013, 43(4):62-67.
[12] CHENG Daizhan, QI Hongsheng, LI Zhiqiang. Analysis and control of Boolean networks: a semi-tensor product approach[M]. London: Springer, 2011:29-36.
[13] CHENG Daizhan, QI Hongsheng, ZHAO Yin. An introduction to semi-tensor product of matrices and its applications[M]. Singapore:World Scientific Publishing Co Pte Ltd, 2012.
[14] CHENG Daizhan, QI Hongsheng, ZHAO Yin. On Boolean control networks—an algebraic approach[C]//Proceedings of the 18th IFAC World Congress. Milano: International Federation of Automatic Control, 2011:8366-8377.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

k-值控制网络的可控性与可观性

Controllability and observability of k-valued control networks

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 7

多维度评价

本文评价

推荐阅读 0

[1]	崔静,梁秋菊. 分数布朗运动驱动的非局部随机积分微分系统的存在性与可控性[J]. 山东大学学报（理学版）, 2017, 52(12): 81-88.
[2]	邢海云,赵建立. 变异机制在网络演化博弈中的应用[J]. 山东大学学报（理学版）, 2016, 51(12): 103-107.
[3]	葛美侠, 李莹, 赵建立, 邢海云. 网络演化博弈的策略一致性[J]. 山东大学学报（理学版）, 2015, 50(11): 113-118.
[4]	程代展,赵寅，徐相如. 混合值逻辑及其应用[J]. 山东大学学报（理学版）, 2011, 46(10): 32-44.
[5]	宋彩芹赵建立王晓东. 三矩阵左半张量积的加权Moore-Penrose[J]. J4, 2009, 44(10): 80-86.
[6]	唐善刚. 广义容斥原理及其应用[J]. J4, 2009, 44(1): 83-90 .
[7]	宋彩芹,赵建立,李东方 . 矩阵左半张量积的(T,S,2)-逆的反序律[J]. J4, 2008, 43(6): 71-76 .