Sampled-data stabilization of probabilistic Boolean control networks

Abstract Probabilistic Boolean networks (PBNs) are discrete-time systems composed of a family of Boolean networks (BNs), between which the PBN switches in a stochastic fashion. In this paper, we address the stabilization of probabilistic Boolean control networks (PBCNs) via a sampled-data state feedback controller (SDSFC). Based on the algebraic representation of logical functions, a necessary and sufficient condition is derived for the existence of SDSFCs for the global stabilization of PBCNs, and the controller is further designed. A biological example is presented to illustrate the effectiveness of the obtained results.

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

[2]  Ettore Fornasini,et al.  On the periodic trajectories of Boolean control networks , 2013, Autom..

[3]  Jinde Cao,et al.  On the Optimal Control of Boolean Control Networks , 2018, SIAM J. Control. Optim..

[4]  Jiandong Zhu,et al.  System decomposition with respect to inputs for Boolean control networks , 2014, Autom..

[5]  Jinde Cao,et al.  On Pinning Synchronization of Directed and Undirected Complex Dynamical Networks , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Michal Linial,et al.  Using Bayesian Networks to Analyze Expression Data , 2000, J. Comput. Biol..

[7]  Fangfei Li,et al.  Pinning Control Design for the Synchronization of Two Coupled Boolean Networks , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[8]  Jinde Cao,et al.  Observability of Boolean control networks , 2018, Science China Information Sciences.

[9]  Daizhan Cheng,et al.  Disturbance decoupling control design for switched Boolean control networks , 2014, Syst. Control. Lett..

[10]  Yongqing Yang,et al.  On sampled-data control for stabilization of genetic regulatory networks with leakage delays , 2015, Neurocomputing.

[11]  D. Cheng,et al.  Analysis and control of Boolean networks: A semi-tensor product approach , 2010, 2009 7th Asian Control Conference.

[12]  Yang Liu,et al.  The equivalence issue of two kinds of controllers in Boolean control networks , 2018, Appl. Math. Comput..

[13]  Yang Liu,et al.  Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems , 2017 .

[14]  Yuzhen Wang,et al.  Output feedback stabilization control design for Boolean control networks , 2013, Autom..

[15]  Zhen Wang,et al.  Event-Triggered Control for the Stabilization of Probabilistic Boolean Control Networks , 2018, Complex..

[16]  Fangfei Li,et al.  Set stabilization for switched Boolean control networks , 2017, Autom..

[17]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[18]  Daizhan Cheng,et al.  A note on observability of Boolean control networks , 2015, 2015 10th Asian Control Conference (ASCC).

[19]  Yang Liu,et al.  Strategy optimization for static games based on STP method , 2018, Appl. Math. Comput..

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

[21]  Yang Liu,et al.  Event-Triggered Control for the Disturbance Decoupling Problem of Boolean Control Networks , 2018, IEEE Transactions on Cybernetics.

[22]  Tianguang Chu,et al.  State feedback stabilization for probabilistic Boolean networks , 2014, Autom..

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

[24]  Young Hoon Joo,et al.  A Note on Sampled-Data Stabilization of LTI Systems With Aperiodic Sampling , 2015, IEEE Transactions on Automatic Control.

[25]  C. Charalambous,et al.  Robust control of uncertain context-sensitive probabilistic Boolean networks. , 2009, IET systems biology.

[26]  Yang Liu,et al.  Nonsingularity of Grain-like cascade FSRs via semi-tensor product , 2017, Science China Information Sciences.

[27]  Aniruddha Datta,et al.  Intervention in context-sensitive probabilistic Boolean networks , 2005, Bioinform..

[28]  Hongwei Chen,et al.  Partial Synchronization of Interconnected Boolean Networks , 2017, IEEE Transactions on Cybernetics.

[29]  Yang Liu,et al.  Stabilization of evolutionary networked games with length-r information , 2018, Appl. Math. Comput..

[30]  Lihua Xie,et al.  Output Regulation of Boolean Control Networks , 2017, IEEE Transactions on Automatic Control.

[31]  Koichi Kobayashi,et al.  Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities , 2017, IEEE Transactions on Neural Networks and Learning Systems.

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

[33]  D. A. Baxter,et al.  Mathematical Modeling of Gene Networks , 2000, Neuron.

[34]  Jinde Cao,et al.  Synchronization of Randomly Coupled Neural Networks With Markovian Jumping and Time-Delay , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  Junan Lu,et al.  Pinning adaptive synchronization of a general complex dynamical network , 2008, Autom..

[36]  Jiandong Zhu,et al.  Kalman decomposition for Boolean control networks , 2015, Autom..

[37]  Zidong Wang,et al.  Pinning controllability of autonomous Boolean control networks , 2016, Science China Information Sciences.

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

[39]  José Claudio Geromel,et al.  Optimal H2 state feedback sampled-data control design of Markov Jump Linear Systems , 2015, Autom..

[40]  Jinde Cao,et al.  Exponential Synchronization of Delayed Neural Networks With Discontinuous Activations , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[41]  Tingwen Huang,et al.  Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks , 2017, IEEE Transactions on Cybernetics.

[42]  Fangfei Li,et al.  Pinning Control Design for the Stabilization of Boolean Networks , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Yuzhen Wang,et al.  Output reachability analysis and output regulation control design of Boolean control networks , 2016, Science China Information Sciences.