Controllability for a special case of multi-level Boolean control networks

This paper investigates controllability problem for multi-level Boolean control networks (BCNs). In this paper, the controllability is investigated and two notions of controllability are presented, i.e. group-controllability and simultaneous-controllability. By resorting to Perron-Frobenius theorem, necessary and sufficient criteria are obtained to guarantee group-controllability and simultaneous-controllability respectively. Finally, a numerical example is presented to show the validness of our main results.

[1]  Harry Eugene Stanley,et al.  Catastrophic cascade of failures in interdependent networks , 2009, Nature.

[2]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[3]  Hong Liu,et al.  Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update , 2014, Scientific Reports.

[4]  M. Ng,et al.  Control of Boolean networks: hardness results and algorithms for tree structured networks. , 2007, Journal of theoretical biology.

[5]  M. Gerstein,et al.  Genomic analysis of the hierarchical structure of regulatory networks , 2006, Proceedings of the National Academy of Sciences.

[6]  Jinde Cao,et al.  On Pinning Controllability of Boolean Control Networks , 2016, IEEE Transactions on Automatic Control.

[7]  M. Gerstein,et al.  Analysis of diverse regulatory networks in a hierarchical context shows consistent tendencies for collaboration in the middle levels , 2010, Proceedings of the National Academy of Sciences.

[8]  Albertha J. M. Walhout,et al.  The interplay between transcription factors and microRNAs in genome‐scale regulatory networks , 2009, BioEssays : news and reviews in molecular, cellular and developmental biology.

[9]  Tianguang Chu,et al.  State Feedback Stabilization for Boolean Control Networks , 2013, IEEE Transactions on Automatic Control.

[10]  H. Ohtsuki,et al.  Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. , 2007, Physical review letters.

[11]  Xingyuan Wang,et al.  Controllability of asynchronous Boolean multiplex control networks. , 2014, Chaos.

[12]  Jinde Cao,et al.  Sampled-Data State Feedback Stabilization of Boolean Control Networks , 2016, Neural Computation.

[13]  Yang Liu,et al.  Feedback Controller Design for the Synchronization of Boolean Control Networks , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[15]  Jerrold E. Marsden,et al.  Controllability for Distributed Bilinear Systems , 1982 .

[16]  M. Margaliot.  Controllability and observability of Boolean control networks , 2012 .

[17]  Jung Yeol Kim,et al.  Correlated multiplexity and connectivity of multiplex random networks , 2011, 1111.0107.

[18]  Mark Gerstein,et al.  Comparing genomes to computer operating systems in terms of the topology and evolution of their regulatory control networks , 2010, Proceedings of the National Academy of Sciences.

[19]  Jinde Cao,et al.  On Controllability of Delayed Boolean Control Networks , 2016, SIAM J. Control. Optim..

[20]  Michael Margaliot,et al.  Observability of Boolean networks: A graph-theoretic approach , 2013, Autom..

[21]  Yang Liu,et al.  Controllability of probabilistic Boolean control networks based on transition probability matrices , 2015, Autom..

[22]  Michael Margaliot,et al.  Controllability of Boolean control networks via the Perron-Frobenius theory , 2012, Autom..

[23]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[24]  B. Drossel,et al.  Number and length of attractors in a critical Kauffman model with connectivity one. , 2004, Physical review letters.

[25]  Jianquan Lu,et al.  Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks , 2014 .

[26]  Daizhan Cheng,et al.  Analysis and Control of Boolean Networks , 2011 .

[27]  Daizhan Cheng,et al.  A Linear Representation of Dynamics of Boolean Networks , 2010, IEEE Transactions on Automatic Control.

[28]  Michael Margaliot,et al.  Minimum-Time Control of Boolean Networks , 2013, SIAM J. Control. Optim..