Necessary and Sufficient Conditions on Pinning Stabilization for Stochastic Boolean Networks

In this paper, the stabilization problem of the Boolean network (BN) with stochastic disturbances via pinning control has been investigated. The necessary and sufficient conditions are given for robust stabilization of a BN with stochastic disturbances. Then, pinning control is considered to stabilize a BN with stochastic disturbances. An algorithm is given to obtain a new stable system and the pinning control, including the pinned nodes, control design, and control adding, is also solved. Finding the minimal number of pinned nodes is further analyzed. The necessary and sufficient conditions are obtained for the solvability of pinning control, based on which some matrices sets are constructed which leads to the necessary and sufficient conditions of pinning $t$ nodes. Furthermore, an algorithm is introduced to search the minimal number of pinned nodes and what exactly they are, which will reduce the computational burden. Examples are given to illustrate the efficiency of the obtained results.

[1]  Tamer Basar,et al.  Stability structures of conjunctive Boolean networks , 2016, Autom..

[2]  Jinde Cao,et al.  On Pinning Controllability of Boolean Control Networks , 2016, IEEE Transactions on Automatic Control.

[3]  Zhengguang Wu,et al.  Mean square stability for Markov jump Boolean networks , 2019, Science China Information Sciences.

[4]  James Lam,et al.  Stability and Stabilization of Boolean Networks With Stochastic Delays , 2019, IEEE Transactions on Automatic Control.

[5]  Tamer Başar,et al.  Controllability of Conjunctive Boolean Networks With Application to Gene Regulation , 2017, IEEE Transactions on Control of Network Systems.

[6]  Tielong Shen,et al.  An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems , 2015, Syst. Control. Lett..

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

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

[9]  Corrado Possieri,et al.  Asymptotic stability in probability for Stochastic Boolean Networks , 2017, Autom..

[10]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[11]  Dan Zhang,et al.  Dissipative Filtering for Switched Fuzzy Systems With Missing Measurements , 2020, IEEE Transactions on Cybernetics.

[12]  Michael Margaliot,et al.  Symbolic dynamics of Boolean control networks , 2013, Autom..

[13]  Yuzhen Wang,et al.  Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks , 2017, SIAM J. Control. Optim..

[14]  Guanghui Wen,et al.  Dissipativity based fault detection for 2D Markov jump systems with asynchronous modes , 2019, Autom..

[15]  Tielong Shen,et al.  A Finite Convergence Criterion for the Discounted Optimal Control of Stochastic Logical Networks , 2018, IEEE Transactions on Automatic Control.

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

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

[18]  Dan Zhang,et al.  Reliable Filter Design of Takagi–Sugeno Fuzzy Switched Systems With Imprecise Modes , 2020, IEEE Transactions on Cybernetics.

[19]  Dan Zhang,et al.  Dissipativity-Based Control for Fuzzy Systems With Asynchronous Modes and Intermittent Measurements , 2020, IEEE Transactions on Cybernetics.

[20]  Jinde Cao,et al.  Pinning Control for the Disturbance Decoupling Problem of Boolean Networks , 2017, IEEE Transactions on Automatic Control.

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

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

[23]  Zheng-Guang Wu,et al.  Asynchronous Stabilization of Boolean Control Networks With Stochastic Switched Signals , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[25]  Wenwu Yu,et al.  Synchronization via Pinning Control on General Complex Networks , 2013, SIAM J. Control. Optim..

[26]  J. Paulsson.  Summing up the noise in gene networks , 2004, Nature.

[27]  Yang Liu,et al.  Controllability of probabilistic Boolean control networks based on transition probability matrices , 2015, Autom..

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

[29]  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.

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

[31]  Michael Margaliot,et al.  Minimum-Time Control of Boolean Networks , 2013, SIAM J. Control. Optim..

[32]  A. Cho.  Physics. Scientific link-up yields 'control panel' for networks. , 2011, Science.

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

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

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

[36]  I. Couzin,et al.  Effective leadership and decision-making in animal groups on the move , 2005, Nature.

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

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