Pinning Stabilization of Probabilistic Boolean Networks With Time Delays

In this article, the stabilization issues for probabilistic Boolean Networks (PBNs) with time delays are discussed. This article’s objective is designing an efficient algorithm to choose suitable nodes to be pinning controlled for PBNs with time delays. By using the semi-tensor product (STP) of matrices, a PBN with time delays can be converted into a discrete-time linear system, and the transition matrix also can be obtained. Then, the necessary and sufficient conditions in the form of algebraic expression are given for the existence and solvability of the pinning feedback controllers with minimum pinning nodes for PBNs with time delays. Besides, three algorithms are proposed for designing and solving minimum pinning controllers.

[1]  M.H. Hassoun,et al.  Fundamentals of Artificial Neural Networks , 1996, Proceedings of the IEEE.

[2]  Lulu Li,et al.  Event-Based Robust Synchronization of Boolean Control Networks , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[4]  Yang Liu,et al.  Set Stability and Stabilization of Switched Boolean Networks With State-Based Switching , 2018, IEEE Access.

[5]  Frank Allgöwer,et al.  Bistable Biological Systems: A Characterization Through Local Compact Input-to-State Stability , 2008, IEEE Transactions on Automatic Control.

[6]  P. Widimsky,et al.  Original research article - Special issue: Acute Ischemic Stroke The importance of time: Time delays in acute stroke , 2016 .

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

[8]  Daizhan Cheng,et al.  On controllability and stabilizability of probabilistic Boolean control networks , 2012, Science China Information Sciences.

[9]  Jianquan Lu,et al.  Asymptotical Stability of Probabilistic Boolean Networks With State Delays , 2020, IEEE Transactions on Automatic Control.

[10]  Ulisses Braga-Neto,et al.  Optimal state estimation for boolean dynamical systems using a boolean Kalman smoother , 2015, 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP).

[11]  Zidong Wang,et al.  Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances , 2007, Syst. Control. Lett..

[12]  Fangfei Li,et al.  Stability of Boolean Networks With Delays Using Pinning Control , 2018, IEEE Transactions on Control of Network Systems.

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

[14]  Jitao Sun,et al.  Further Investigate the Stability of Complex-Valued Recurrent Neural Networks With Time-Delays , 2014 .

[15]  D. A. Baxter,et al.  Modeling transcriptional control in gene networks—methods, recent results, and future directions , 2000, Bulletin of mathematical biology.

[16]  Li Yu,et al.  Pinning Stabilization of Stochastic Networks With Finite States via Controlling Minimal Nodes. , 2020, IEEE transactions on cybernetics.

[17]  Jianquan Lu,et al.  Pinning Stabilization of Boolean Control Networks via a Minimum Number of Controllers , 2021, IEEE Transactions on Cybernetics.

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

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

[20]  Michael Margaliot,et al.  A Polynomial-Time Algorithm for Solving the Minimal Observability Problem in Conjunctive Boolean Networks , 2017, IEEE Transactions on Automatic Control.

[21]  Jinde Cao,et al.  Stability and Stabilization in Probability of Probabilistic Boolean Networks , 2021, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Jinde Cao,et al.  On pinning reachability of probabilistic Boolean control networks , 2019, Science China Information Sciences.

[23]  Michael Margaliot,et al.  Minimal Controllability of Conjunctive Boolean Networks is NP-Complete , 2017, Autom..

[24]  Tielong Shen,et al.  Policy Iteration Algorithm for Optimal Control of Stochastic Logical Dynamical Systems , 2018, IEEE Transactions on Neural Networks and Learning Systems.

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

[26]  Ettore Fornasini,et al.  Optimal Control of Boolean Control Networks , 2014, IEEE Transactions on Automatic Control.

[27]  Yuanyuan Li,et al.  On Robust Synchronization of Drive-Response Boolean Control Networks with Disturbances , 2018, Mathematical Problems in Engineering.

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