Controllability and optimal control of a temporal Boolean network

This paper investigates the controllability and optimal control of a temporal Boolean network, where the time delays are time variant. First, using the theory of semi-tensor product of matrices, the logical systems can be converted into a discrete time variant system. Second, necessary and sufficient conditions for the controllability via two types of controls are provided respectively. Third, optimal control design algorithms are presented. Finally, examples are given to illustrate the proposed results.

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

[2]  Daizhan Cheng,et al.  Optimal Control of Logical Control Networks , 2011, IEEE Transactions on Automatic Control.

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

[4]  Fangfei Li,et al.  Observability of Boolean Control Networks With State Time Delays , 2011, IEEE Transactions on Neural Networks.

[5]  Li Liu,et al.  Finite-time stability of linear time-varying singular systems with impulsive effects , 2008, Int. J. Control.

[6]  Yurong Liu,et al.  State estimation for jumping recurrent neural networks with discrete and distributed delays , 2009, Neural Networks.

[7]  Michael Margaliot,et al.  A Maximum Principle for Single-Input Boolean Control Networks , 2011, IEEE Transactions on Automatic Control.

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

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

[10]  Fangfei Li,et al.  Controllability of Boolean control networks with time delays in states , 2011, Autom..

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

[12]  Zidong Wang,et al.  An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series , 2009, TCBB.

[13]  Daizhan Cheng,et al.  Algebraic Approach to Dynamics of Multivalued Networks , 2010, Int. J. Bifurc. Chaos.

[14]  Zidong Wang,et al.  Sampled‐data H∞ filtering for stochastic genetic regulatory networks , 2011 .

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

[16]  Jitao Sun,et al.  Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects , 2010, J. Frankl. Inst..

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

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

[19]  B. Goodwin.  Temporal organization in cells , 1963 .

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

[21]  Frank L. Lewis,et al.  2009 Special Issue: Neural network approach to continuous-time direct adaptive optimal control for partially unknown nonlinear systems , 2009 .

[22]  Donald C. Wunsch,et al.  Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization , 2007, Neural Networks.

[23]  Vasant Honavar,et al.  Temporal Boolean Network Models of Genetic Networks and their Inference from Gene Expression Time Series , 2001, Complex Syst..

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

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