Finite-Time Controllability and Set Controllability of Impulsive Probabilistic Boolean Control Networks

This paper addresses the finite-time controllability and set controllability of impulsive probabilistic Boolean control networks (IPBCNs). Firstly, using the algebraic state space representation (ASSR) method, the transition probability matrix of IPBCNs is established. Secondly, a kind of finite step reachability matrix with probability one is constructed, based on which, several effective criteria are proposed for the finite-time controllability with probability one of IPBCNs. Thirdly, a necessary and sufficient condition is presented for the finite-time set controllability with probability one of IPBCNs by constructing the set controllability probability distribution vector. Finally, the obtained results are extended to switching topology case.

[1]  Haitao Li,et al.  A Control Lyapunov Function Approach to Feedback Stabilization of Logical Control Networks , 2019, SIAM J. Control. Optim..

[2]  Aniruddha Datta,et al.  Optimal infinite horizon control for probabilistic Boolean networks , 2006, 2006 American Control Conference.

[3]  Zhaojing Wu,et al.  Stability Criteria of Random Nonlinear Systems and Their Applications , 2015, IEEE Transactions on Automatic Control.

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

[5]  Krishnan Balachandran,et al.  Controllability of nonlinear stochastic neutral impulsive systems , 2009 .

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

[7]  Xiaodi Li,et al.  Controllability for a class of semilinear fractional evolution systems via resolvent operators , 2019, Communications on Pure & Applied Analysis.

[8]  Edward R. Dougherty,et al.  Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks , 2003, Comparative and functional genomics.

[9]  Fangfei Li,et al.  Controllability of probabilistic Boolean control networks , 2011, Autom..

[10]  Jianquan Lu,et al.  Boolean-network-based approach for construction of filter generators , 2020, Science China Information Sciences.

[11]  Weihua Gui,et al.  Set reachability and observability of probabilistic Boolean networks , 2019, Autom..

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

[13]  Jitao Sun,et al.  Asymptotic stability of differential systems with impulsive effects suffered by logic choice , 2015, Autom..

[14]  Jinde Cao,et al.  Synchronization of master-slave Boolean networks with impulsive effects: Necessary and sufficient criteria , 2014, Neurocomputing.

[15]  Jitao Sun,et al.  Observability analysis of Boolean control networks with impulsive effects , 2011 .

[16]  Yang Liu,et al.  Controllability of Boolean control networks with impulsive effects and forbidden states , 2014 .

[17]  Oyelami Benjamin Oyediran.  δ-CONTROLLABILITY OF IMPULSIVE SYSTEMS AND APPLICATIONS TO SOME PHYSICAL AND BIOLOGICAL CONTROL SYSTEM , 2013 .

[18]  Daizhan Cheng,et al.  Observability of Boolean networks via set controllability approach , 2018, Syst. Control. Lett..

[19]  Nazim I. Mahmudov.  Controllability of linear stochastic systems , 2001, IEEE Trans. Autom. Control..

[20]  Xiaojing Xu,et al.  Finite-time stability analysis of stochastic switched boolean networks with impulsive effect , 2019, Appl. Math. Comput..

[21]  Zidong Wang,et al.  State Estimation for Stochastic Time-Varying Boolean Networks , 2020, IEEE Transactions on Automatic Control.

[22]  Yang Tang,et al.  Input-to-state stability for nonlinear systems with stochastic impulses , 2020, Autom..

[23]  Fangfei Li,et al.  Stability and stabilization of Boolean networks with impulsive effects , 2012, Syst. Control. Lett..

[24]  Xiaodong Li,et al.  Stability Analysis of Boolean Networks With Stochastic Function Perturbations , 2019, IEEE Access.

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

[26]  R. E. Kalman,et al.  Controllability of linear dynamical systems , 1963 .

[27]  Fuad E. Alsaadi,et al.  Robust set stabilization of Boolean control networks with impulsive effects , 2018, Nonlinear Analysis: Modelling and Control.

[28]  Fuad E. Alsaadi,et al.  Output tracking control of Boolean control networks with impulsive effects , 2018 .

[29]  Fuad E. Alsaadi,et al.  Control design for output tracking of delayed Boolean control networks , 2018, J. Comput. Appl. Math..

[30]  Weihua Gui,et al.  Sampled-Data State-Feedback Stabilization of Probabilistic Boolean Control Networks: A Control Lyapunov Function Approach , 2020, IEEE Transactions on Cybernetics.

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

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

[33]  Nazim I. Mahmudov,et al.  On Concepts of Controllability for Deterministic and Stochastic Systems , 1999 .

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

[35]  Bo Wu,et al.  A minimum-time control for Boolean control networks with impulsive disturbances , 2016, Appl. Math. Comput..

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

[37]  Fuad E. Alsaadi,et al.  Stochastic stability and stabilization of n-person random evolutionary Boolean games , 2017, Appl. Math. Comput..

[38]  Xiaodi Li,et al.  Persistent impulsive effects on stability of functional differential equations with finite or infinite delay , 2018, Appl. Math. Comput..

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

[40]  Hamid Reza Karimi,et al.  Stability of Stochastic Nonlinear Systems With State-Dependent Switching , 2013, IEEE Transactions on Automatic Control.

[41]  Yating Zheng,et al.  State-feedback set stabilization of logical control networks with state-dependent delay , 2020, Science China Information Sciences.

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

[43]  Fuad E. Alsaadi,et al.  Algebraic formulation and topological structure of Boolean networks with state-dependent delay , 2019, J. Comput. Appl. Math..

[44]  S. Bhat.  Controllability of Nonlinear Systems , 2022 .

[45]  Xiao Chen,et al.  Finite-time stability of genetic regulatory networks with impulsive effects , 2017, Neurocomputing.

[46]  Jinde Cao,et al.  Stabilization of Boolean control networks with stochastic impulses , 2019, J. Frankl. Inst..

[47]  Jinling Liang,et al.  Local Synchronization of Interconnected Boolean Networks With Stochastic Disturbances , 2020, IEEE Transactions on Neural Networks and Learning Systems.

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

[49]  Lijun Zhang,et al.  Invertibility and nonsingularity of Boolean control networks , 2015, Autom..

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

[51]  Jianquan Lu,et al.  Synchronization of drive-response Boolean control networks with impulsive disturbances , 2020, Appl. Math. Comput..

[52]  Jitao Sun,et al.  Stabilization, Controllability and Optimal Control of Boolean Networks With Impulsive Effects and State Constraints , 2015, IEEE Transactions on Automatic Control.

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

[54]  Xiaoming Hu,et al.  Set Stability and Controllability for Switched Non-homogeneous Linear Systems , 2006, 2006 Chinese Control Conference.

[55]  Feiqi Deng,et al.  Operator-Type Stability Theorem for Retarded Stochastic Systems With Application , 2016, IEEE Transactions on Automatic Control.

[56]  Haitao Li,et al.  Set stability and synchronization of logical networks with probabilistic time delays , 2018, J. Frankl. Inst..

[57]  Edward R. Dougherty,et al.  Effect of Function Perturbation on the Steady-State Distribution of Genetic Regulatory Networks: Optimal Structural Intervention , 2008, IEEE Transactions on Signal Processing.