# 一篇在审的博士学位论文 精选

1谁说我们没有创新

2别人眼里的矩阵半张量积

3矩阵半张量积向何处去

[1] D. Cheng, H. Qi, Z. li, Analysis and Control fo Boolean Networks, Springer-Verlag, 2011.

[2] D. Cheng, H. Qi, A linear representation of dynamics of Boolean networks, IEEE Trans. Aut. Contr. , Vol. 55, 2251-2258, 2010.

[3] D. Cheng, Input-state approach to Boolean networks, IEEE Trans. Neural Networks, Vol. 20, 512-521, 2009.

[4] D. Cheng, H. Qi, State-space analysis of Boolean networks, IEEE Trans. Neural Networks, Vol. 21, 584-594, 2010.

[5] D. Cheng, Z. Li, H. Qi, Realization of Boolean control networks, Automatica, Vol. 46, 62-69, 2010.

[6] D. Cheng, H. Qi, Controllability and observability of Boolean control networks, Automatica, Vol. 45, 1659-1667, 2009.

[7] D. Cheng, Disturbance decoupling of Boolean control networks, IEEE Trans. Aut. Contr. , Vol. 56, 2-10, 2011.

[8] D. Cheng, H. Qi, Z. Li, J. Liu, Stability and stabilization of Boolean networks, Int. J. Robust Nonlin. Contr. , Vol. 21, 134-156, 2011.

[9] Y. Zhao, Z. Li, D. Cheng, Optimal control of logical control networks, IEEE Trans. Aut. Contr. , Vol. 56, 1766-1776, 2011.

[10] D. Cheng, Y. Zhao, Identification of Boolean control networks, Automatica, Vol. 47, 702-710, 2011.

[11] D. Cheng, H. Qi, Y. Zhao, Analysis and control of general logical networks An algebraic approach, Annual Reviews in Contr. , Vol. 36, 11-25, 2012.

[12] Y. Wang, C. Zhang, Z. Liu, A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems, Automaitca, Vol. 48, 1227-1236, 2012.

[13] H. Li, Y. Wang, Z. Liu, Existence and number of fixed pints of Boolean transformations via the semi-tensor product method, Appl. Math. Letters, Vol. 25, 1142-1147, 2012.

[14] Z. Liu, Y. Wang, Disturbance decoupling of mix-valued logical networks via the semi-tensor product method, Automatica, Vol. 48, 1839-1844, 2012.

[15] F. Li, J. Sun, Cotrollability and optimal control of a temporal Boolean network, Neural Networks, Vol. 34, 10-17, 2012.

[16] H. Li, Y. Wang, On reachability and controllability of switched Boolean control networks, Automatica, Vol. 48, 2917-2922, 2012.

[17] E. Fornasini, M. E. Valcher, Observability, reconstructibility and state observers of Boolean control networks, IEEE Trans. Aut. Contr. , Vol. 58, 1390-1401, 2013.

[18] F. Li, J. Sun, Controllability of higher order Boolean control networks, Appl. Math. Comput. , Vol. 219, 158-169, 2012.

[19] H. Chen, J. Sun, A new approach for global controllability of higher order Boolean control network, Neural Networks, Vol. 39, 12-17, 2013.

[20] E. Fornasini, M. E. Valcher, On the periodic trajectories of Boolean control networks, Automatica, Vol. 49, 1506-1509, 2013.

[21]H. Li, Y. Wang, Consistent stabilizability of switched Boolean networks, Neural Networks, Vol. 46, 183-189, 2013.

[22] R. Li, T. Chu, Complete synchronization of Boolean networks, IEEE Trans. Neural Netw. Learn. Syst. , Vol. 23, 840-846, 2012.

[23] R. Li, M. Yang, T. Chu, Synchronization of Boolean networks with time delays, Appl. Math. Comput. , Vol. 219, 917-927, 2012.

[24] R. Li, M. Yang, T. Chu, Synchronization design of Boolean networks via the semi-tensor product method, IEEE Trans. Neural Netw. Learn. Syst. , Vol. 24, 996-1001, 2013.

[25] R. Li, M. Yang, T. Chu, State feedback stabilization for Boolean control networks, IEEE Trans. Aut. Contr. , Vol. 58, 1853-1857, 2013.

[26] D. Cheng, X. Xu, Bi-decomposition of multi-valued logical functions and its applications, Automatica, Vol. 49, 1979-1985, 2013.

[27] D. Cheng, J. Feng, H. Lv, Solving fuzzy relational equations via semi-tensor product, IEEE Trans. Fuzzy Syst. , Vol. 20, 390-396, 2012.

[28] M. Meng, J. Feng, Synchronization of interconnected multi-valued logical networks, Asian J. Contr. , to appear.

[29] L. Zhan, K. Zhang, Controllability and observability of Boolean control networks with time-variant delays in states, IEEE Trans. Neural Netw. Learn. Syst. , Vol. 24, 1478-1484, 2013.

[30] X. Xu, Y. Hong, Matrix approach to model matching of asynchrollous sequential machines, IEEE Trans. Aut. Contr. , on line: http://ieee.org/stamp/stamp.jsp?tp=&arnumber=6507639.

[31] M. Yang, R. Li, T. Chu, Controller design for disturbance decoupling of Boolean control networks, Automatica, Vol. 49, No. 1, 273-277, 2013.

[32] Y. Zhao, J. Kim, M. Filippone, Aggregation algorithm towards large-scale Boolean network analysis, IEEE Trans. Aut. Contr. , on line: http://ieee.org/stamp/stamp. jsp?tp=&arnumber=6365758.

[33] L. Zhang, J. Feng, Mix-valued logic based formation control, Int. J. Contr. , Vol. 89, 1191-1199, 2013.

[34] D. Cheng, F. He, H. Qi, T. Xu, F. He, Modeling, analysis and control of networked evolutionary games, http://lsc.amss.ac.cn/~dcheng/preprint/NTGAME02.pdf (IEEE TAC, under revision).

[35] 王树和, 《数学聊斋》, 科学出版社, 北京, 2008.

Boolean networks (BNs) are discrete-time dynamical systems with Boolean state variables. BNs are recently attracting considerable interest as computational models for biological systems and, in particular, as models of gene regulating networks. Boolean control networks (BCNs) are Boolean networks with Boolean inputs. Daizhan Cheng developed an algebraic state-space representation for BCNs using the semi-tensor product of matrices. This representation proved quite useful for studying BCNs in a control-theoretic framework.

In this work we use the algebraic state-space representation to study several control-theoretic problems for BNs and BCNs includingoptimal control, minimum-time control, controllability, and observability. Addressing these problems may lead to a better understanding of genetic circuits and the intrinsic control in biological systems using exogenous inputs.

Daizhan Cheng and his colleagues developed an algebraic representation of BNs/BCNs [30]. We give a detailed description of this representation in Chapter 2. This new approach stimulated considerable research in the control theory of BNs/BCNs. Examples includefinding the number of fixed points and cycles, transient period and basin of attractors of BNs and BCNs [28, 23]; state-space analysis of BNs [29]; realization of BCNs [26]; controllability and observabiity [27]; disturbance decoupling [24]; stability and stabilization [31]; infinite horizon optimal control [131]; identification of BCNs [33] and more. A good survey of these works can be found in [32].

More recently the algebraic representation of BNs/BCNs has been used to investigate the following problemsthe maximum stable set and vertex coloring problems of graphs with application to the group consensus of multi-agent systems [126], the existence and number of fixed points of Boolean transformations [88], disturbance decoupling in mix-valued logical networks [96], controllability and optimal control of a temporal Boolean networks [96], controllability and optimal control of a temporal Boolean network [84], reachability and controllability of switched BCNs [86], observability and reconstructibility properties of BNs and BCNs [47], controllability of higher-order BCNs [85, 22], periodic structure of the state trajectories of BNs and BCNs [48], consistent stabilizability of switched BNs [87], synchronization of BNs with and without thime delays [89, 90, 92], and state feedback stabilization [91].

https://blog.sciencenet.cn/blog-660333-719184.html