Controllability of probabilistic Boolean control networks

This paper deals with the controllability of probabilistic Boolean control networks. First, a survey on the semi-tensor product approach to probabilistic Boolean networks is given. Second, the controllability of probabilistic Boolean control networks via two kinds inputs is studied. Finally, examples are given to show the efficiency of the obtained results.

[1]  D. Cheng,et al.  Stability and stabilization of Boolean networks , 2011 .

[2]  Xi Chen,et al.  Finding optimal control policy in Probabilistic Boolean Networks with hard constraints by using integer programming and dynamic programming , 2010, BIBM.

[3]  John Maloney,et al.  Finding Cycles in Synchronous Boolean Networks with Applications to Biochemical Systems , 2003, Int. J. Bifurc. Chaos.

[4]  Daizhan Cheng,et al.  Input-State Approach to Boolean Networks , 2009, IEEE Transactions on Neural Networks.

[5]  T. Akutsu,et al.  Optimal control policy for probabilistic Boolean networks with hard constraints. , 2009, IET systems biology.

[6]  B. Samuelsson,et al.  Superpolynomial growth in the number of attractors in Kauffman networks. , 2003, Physical review letters.

[7]  Daizhan Cheng,et al.  Input-state incidence matrix of Boolean control networks and its applications , 2010, Syst. Control. Lett..

[8]  A. Datta,et al.  On approximate stochastic control in genetic regulatory networks. , 2007, IET systems biology.

[9]  Michael K. Ng,et al.  An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks , 2007, Bioinform..

[10]  Luis G. Vargas,et al.  An optimization-based approach for the design of Bayesian networks , 2008, Math. Comput. Model..

[11]  Edward R. Dougherty,et al.  Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks , 2003, Comparative and functional genomics.

[12]  Edward R. Dougherty,et al.  Steady-state probabilities for attractors in probabilistic Boolean networks , 2005, Signal Process..

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

[14]  Daizhan Cheng,et al.  Controllability and observability of Boolean control networks , 2009, Autom..

[15]  Xiaoming Hu,et al.  Stabilization of random Boolean networks , 2010, 2010 8th World Congress on Intelligent Control and Automation.

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

[17]  Daizhan Cheng,et al.  Realization of Boolean control networks , 2010, Autom..

[18]  John Maloney,et al.  Scalar equations for synchronous Boolean networks with biological applications , 2004, IEEE Transactions on Neural Networks.

[19]  James Lam,et al.  Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances , 2008, IEEE Transactions on Automatic Control.

[20]  Jitao Sun,et al.  Complete controllability of impulsive stochastic integro-differential systems , 2010, Autom..

[21]  Aniruddha Datta,et al.  Optimal infinite horizon control for probabilistic Boolean networks , 2006, 2006 American Control Conference.

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

[23]  Roger W. Brockett,et al.  Finite Controllability of Infinite-Dimensional Quantum Systems , 2010, IEEE Transactions on Automatic Control.

[24]  Edward R. Dougherty,et al.  Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks , 2002, Bioinform..

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