SCIENCE CHINA Information Sciences, Volume 62 , Issue 1 : 012208(2019) https://doi.org/10.1007/s11432-018-9447-4

Further results on dynamic-algebraic Boolean control networks

More info
  • ReceivedMar 7, 2018
  • AcceptedMay 3, 2018
  • PublishedDec 19, 2018



This work was supported by National Natural Science Foundation of China (Grant No. 61773371).


[1] Kauffman S A. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 1969, 22: 437-467 CrossRef Google Scholar

[2] Akutsu T, Miyano S, Kuhara S. Inferring qualitative relations in genetic networks and metabolic pathways. Bioinformatics, 2000, 16: 727-734 CrossRef Google Scholar

[3] Albert R, Barabási A L. Dynamics of Complex Systems: Scaling Laws for the Period of Boolean Networks. Phys Rev Lett, 2000, 84: 5660-5663 CrossRef PubMed ADS Google Scholar

[4] Zhang S Q, Ching W K, Chen X. Generating probabilistic Boolean networks from a prescribed stationary distribution. Inf Sci, 2010, 180: 2560-2570 CrossRef Google Scholar

[5] Zhao Q. A remark on “scalar equations for synchronous Boolean networks with biological applications" by C. Farrow, J. Heidel, J. Maloney, and J. Rogers. IEEE Trans Neural Netw, 2005, 16: 1715-1716 CrossRef PubMed Google Scholar

[6] Cheng D Z. Semi-tensor product of matrices and its application to Morgen's problem. Sci China Ser F-Inf Sci, 2001, 44: 195--212. Google Scholar

[7] Cheng D, Qi H. A Linear Representation of Dynamics of Boolean Networks. IEEE Trans Automat Contr, 2010, 55: 2251-2258 CrossRef Google Scholar

[8] Zhao J, Chen Z, Liu Z. Modeling and analysis of colored petri net based on the semi-tensor product of matrices. Sci China Inf Sci, 2018, 61: 010205 CrossRef Google Scholar

[9] Liu G, Jiang C. Observable liveness of Petri nets with controllable and observable transitions. Sci China Inf Sci, 2017, 60: 118102 CrossRef Google Scholar

[10] Cheng D, Qi H. Controllability and observability of Boolean control networks. Automatica, 2009, 45: 1659-1667 CrossRef Google Scholar

[11] Cheng D, Li Z, Qi H. Realization of Boolean control networks. Automatica, 2010, 46: 62-69 CrossRef Google Scholar

[12] Cheng D, Zhao Y. Identification of Boolean control networks. Automatica, 2011, 47: 702-710 CrossRef Google Scholar

[13] Cheng D, Qi H, Li Z. Stability and stabilization of Boolean networks. Int J Robust NOnlinear Control, 2011, 21: 134-156 CrossRef Google Scholar

[14] Cheng D. Disturbance Decoupling of Boolean Control Networks. IEEE Trans Automat Contr, 2011, 56: 2-10 CrossRef Google Scholar

[15] Liu Y, Li B, Lu J. Pinning Control for the Disturbance Decoupling Problem of Boolean Networks. IEEE Trans Automat Contr, 2017, 62: 6595-6601 CrossRef Google Scholar

[16] Meng M, Lam J, Feng J. l1-gain analysis and model reduction problem for Boolean control networks. Inf Sci, 2016, 348: 68-83 CrossRef Google Scholar

[17] Cheng D, Qi H, Liu T. A note on observability of Boolean control networks. Syst Control Lett, 2016, 87: 76-82 CrossRef Google Scholar

[18] Zhang K Z, Zhang L J. Observability of Boolean control networks: a unified approach based on the theories of finite automata. IEEE Trans Autom Control, 2014, 61: 6854--6861. Google Scholar

[19] Zhu Q, Liu Y, Lu J. Observability of Boolean control networks. Sci China Inf Sci, 2018, 61: 092201 CrossRef Google Scholar

[20] Daizhan Cheng . Input-state approach to Boolean networks.. IEEE Trans Neural Netw, 2009, 20: 512-521 CrossRef PubMed Google Scholar

[21] Zhao Y, Qi H, Cheng D. Input-state incidence matrix of Boolean control networks and its applications. Syst Control Lett, 2010, 59: 767-774 CrossRef Google Scholar

[22] Liu G B, Xu S Y, Wei Y L, et al. New insight into reachable set estimation for uncertain singular time-delay systems. Appl Math Comput, 2018, 320: 769--780. Google Scholar

[23] Liu L, Li H, Liu C. Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions. J NOnlinear Sci Appl, 2017, 10: 243-262 CrossRef Google Scholar

[24] Liu L S, Sun F L, Zhang X G, et al. Bifurcation analysis for a singular differential system with two parameters via to topological degree theory. Nonlinear Anal Model Control, 2017, 22: 31--50. Google Scholar

[25] Zheng Z, Kong Q. Friedrichs extensions for singular Hamiltonian operators with intermediate deficiency indices. J Math Anal Appl, 2018, 461: 1672-1685 CrossRef Google Scholar

[26] Cheng D Z, Zhao Y, Xu X R. Mix-valued logic and its applications. J Shandong Univ (Natl Sci), 2011, 46: 32--44. Google Scholar

[27] Feng J E, Yao J, Cui P. Singular Boolean networks: Semi-tensor product approach. Sci China Inf Sci, 2012, 22 CrossRef Google Scholar

[28] Meng M, Feng J. Optimal control problem of singular Boolean control networks. Int J Control Autom Syst, 2015, 13: 266-273 CrossRef Google Scholar

[29] Liu Y, Li B, Chen H. Function perturbations on singular Boolean networks. Automatica, 2017, 84: 36-42 CrossRef Google Scholar

[30] Qiao Y, Qi H, Cheng D. Partition-Based Solutions of Static Logical Networks With Applications.. IEEE Trans Neural Netw Learning Syst, 2018, 29: 1252-1262 CrossRef PubMed Google Scholar

[31] Guo Y X. Nontrivial periodic solutions of nonlinear functional differential systems with feedback control. Turkish J Math, 2010, 34: 35. Google Scholar

[32] Ma C, Li T, Zhang J. Consensus control for leader-following multi-agent systems with measurement noises. J Syst Sci Complex, 2010, 23: 35-49 CrossRef Google Scholar

[33] Qin H, Liu J, Zuo X. Approximate controllability and optimal controls of fractional evolution systems in abstract spaces. Adv Diff Equ, 2014, 2014: 322 CrossRef Google Scholar

[34] Sun W, Peng L. Observer-based robust adaptive control for uncertain stochastic Hamiltonian systems with state and input delays. NA, 2014, 19: 626-645 CrossRef Google Scholar

[35] Khatri C G, Rao C R. Solutions to some functional equations and their applications to characterization of probability distributions. Indian J Stat Ser A, 1968, 30: 167--180. Google Scholar

[36] Heidel J, Maloney J, Farrow C. Finding Cycles in Synchronous Boolean Networks with Applications to Biochemical Systems. Int J Bifurcation Chaos, 2003, 13: 535-552 CrossRef ADS Google Scholar

[37] Ashenhurst R L. The decomposition of switching functions. In: Proceedings of an International Symposium on the Theory of Switching, 1957. 74--116. Google Scholar

[38] Curtis H A. A New Approach to the Design of Switching Circuits. New York: Van Nostrand Reinhold, 1962. Google Scholar

[39] Sasao T, Butler J T. On Bi-Decompositions of Logic Functions. Technical Report, DTIC Document, 1997. Google Scholar

[40] Sasao T. Application of multiple-valued logic to a serial decomposition of plas. In: Proceedings of the 19th International Symposium on Multiple-Valued Logic, 1989. 264--271. Google Scholar

[41] Muroga S. Logic Design and Switching Theory. New York: Wiley, 1979. Google Scholar