Minimum-Triggering Control for Probabilistic Boolean Networks

Considering that a network is generally not globally stable, it is of great significance to design several proper stabilizers. In this paper, we investigate the minimum-triggering control for probabilistic Boolean networks, that is, designing an event-triggered strategy under which the whole network can realize stabilization within globally minimal control times. To this end, a graph-based algorithm is developed and the time complexity is bounded by O(2n+m), where n and m are respectively the number of state nodes and control inputs. Furthermore, an illustrative example is presented to verify the application of the obtained theoretical results.

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

[2]  Fuad E. Alsaadi,et al.  Output Regulation of Boolean Control Networks With Nonuniform Sampled-Data Control , 2019, IEEE Access.

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

[4]  Edward R. Dougherty,et al.  From Boolean to probabilistic Boolean networks as models of genetic regulatory networks , 2002, Proc. IEEE.

[5]  Jinde Cao,et al.  Stabilization of Boolean Control Networks Under Aperiodic Sampled-Data Control , 2018, SIAM J. Control. Optim..

[6]  Weihua Gui,et al.  Stability and Set Stability in Distribution of Probabilistic Boolean Networks , 2019, IEEE Transactions on Automatic Control.

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

[8]  Shun-ichi Azuma,et al.  Structural oscillatority analysis of Boolean networks , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[9]  Yun-Bo Zhao,et al.  Probabilistic Boolean Network Modelling and Analysis Framework for mRNA Translation , 2016, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

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

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

[12]  Jinde Cao,et al.  Robust Event-Triggered Control Invariance of Probabilistic Boolean Control Networks , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Luis Anido Rifón,et al.  Probabilistic Boolean network modeling of an industrial machine , 2018, J. Intell. Manuf..

[14]  Daniel W. C. Ho,et al.  Global robust stability and stabilization of Boolean network with disturbances , 2017, Autom..

[15]  Jinde Cao,et al.  Stabilization of logical control networks: an event-triggered control approach , 2019, Science China Information Sciences.

[16]  Wai-Ki Ching,et al.  Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable , 2019, Frontiers of Information Technology & Electronic Engineering.

[17]  Ettore Fornasini,et al.  Output feedback stabilization of Boolean control networks , 2015, Autom..

[18]  Jinde Cao,et al.  Sampled-Data Set Stabilization of Impulsive Boolean Networks Based on a Hybrid Index Model , 2020, IEEE Transactions on Control of Network Systems.

[19]  Yang Liu,et al.  On algorithms for state feedback stabilization of Boolean control networks , 2017, Autom..

[20]  Jinde Cao,et al.  Set Stabilization of Boolean Control Networks With Impulsive Effects: An Event-Triggered Approach , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[21]  Yuzhen Wang,et al.  Further results on feedback stabilization control design of Boolean control networks , 2017, Autom..

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

[23]  Daizhan Cheng,et al.  From Boolean game to potential game , 2018, Autom..

[24]  Tielong Shen,et al.  Optimal control of Boolean control networks with average cost: A policy iteration approach , 2019, Autom..

[25]  Guodong Zhao,et al.  Leader–Follower Consensus of Multiagent Systems With Time Delays Over Finite Fields , 2019, IEEE Transactions on Cybernetics.

[26]  Gang Feng,et al.  Stability and $l_1$ Gain Analysis of Boolean Networks With Markovian Jump Parameters , 2017, IEEE Transactions on Automatic Control.

[27]  Ettore Fornasini,et al.  Observability, Reconstructibility and State Observers of Boolean Control Networks , 2013, IEEE Transactions on Automatic Control.