|
|
- 2015
k-值控制网络的可控性与可观性
|
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kn+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.
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 kn+m to kn. Aslo, a sufficient condition for observabilitywas obtained, which can be computed easily
| [1] | CHENG Daizhan, QI Hongsheng, LI Zhiqiang. Identification of Boolean control networks[M]//Analysis and Control of Boolean Networks. London:Springer, 2011:389-407. |
| [2] | 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. |
| [3] | CHENG Daizhan. Semi-tensor product of matrices and its application to Margan's problems[J]. Science in China, 2001, 44(3):195-212. |
| [4] | LI Fangfei, SUN Jitao. Stability and stabilization of multivalued logical networks[J]. Nonlinear Analysis: Real World Applications, 2011, 12(6):3701-3712. |
| [5] | 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. |
| [6] | 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. |
| [7] | CHENG Daizhan, QI Hongsheng, LI Zhiqiang. Analysis and control of Boolean networks: a semi-tensor product approach[M]. London: Springer, 2011:29-36. |
| [8] | 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. |
| [9] | 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. |
| [10] | 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. |
| [11] | ZHAO Yin, CHENG Daizhan. On controllability and stabilizability of probabilistic Boolean control networks[J]. Science China Information Sciences, 2014, 57(1):1-14. |
| [12] | KAUFFMAN A S. Metabolic stability and epigenesis in randomly constructed genetic nets[J]. Theoretical Biology, 1969, 22(3):437-467. |
| [13] | CHENG Daizhan, QI Hongsheng. Input-state approach to Boolean networks[J]. IEEE Transactions on Neuralnetworks, 2009, 20(3):512-521. |
| [14] | 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. |
