Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks

Abstract In this paper, we investigate the static output feedback set stabilization for context-sensitive probabilistic Boolean control networks (CS-PBCNs) via the semi-tensor product of matrices. An algorithm for finding the largest control invariant set with probability one is obtained by the algebraic representations of logical dynamics. Based on the analysis of the set stabilization, necessary and sufficient conditions for S-stabilization are obtained. Static output feedback controllers are designed to achieve S-stabilization for a CS-PBCN. At last, examples to study metastatic melanoma are given to show the effectiveness of our main results.

[1]  Huimin Xiao,et al.  Weak reachability of probabilistic boolean control networks , 2015, 2015 International Conference on Advanced Mechatronic Systems (ICAMechS).

[2]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[3]  Bo Wu,et al.  A Halanay-type inequality approach to the stability analysis of discrete-time neural networks with delays , 2015, Appl. Math. Comput..

[4]  Tianguang Chu,et al.  Synchronization of Boolean networks with time delays , 2012, Appl. Math. Comput..

[5]  Yuxia Li,et al.  Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay , 2017, Int. J. Bifurc. Chaos.

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

[7]  Yang Liu,et al.  Feedback Controller Design for the Synchronization of Boolean Control Networks , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Koichi Kobayashi,et al.  An integer programming approach to optimal control problems in context-sensitive probabilistic Boolean networks , 2011, Autom..

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

[10]  Yun Niu,et al.  Optimal control for context-sensitive probabilistic Boolean networks with perturbation using probabilisitic model checking , 2016, 2016 IEEE International Conference on Bioinformatics and Biomedicine (BIBM).

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

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

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

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

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

[16]  Yuzhen Wang,et al.  State feedback based output tracking control of probabilistic Boolean networks , 2016, Inf. Sci..

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

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

[19]  Lihua Xie,et al.  Finite automata approach to observability of switched Boolean control networks , 2016 .

[20]  Daizhan Cheng,et al.  A Linear Representation of Dynamics of Boolean Networks , 2010, IEEE Transactions on Automatic Control.

[21]  Haipeng Peng,et al.  Principle for performing attractor transits with single control in Boolean networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

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

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

[26]  Haipeng Peng,et al.  Attractor Transformation by Impulsive Control in Boolean Control Network , 2013 .

[27]  Daizhan Cheng,et al.  Disturbance Decoupling of Boolean Control Networks , 2011, IEEE Transactions on Automatic Control.

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

[29]  Jitao Sun,et al.  Stability and stabilisation of context-sensitive probabilistic Boolean networks , 2014 .

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

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

[32]  Fangfei Li,et al.  Controllability of higher order Boolean control networks , 2012, Appl. Math. Comput..

[33]  Tianguang Chu,et al.  Controller design for disturbance decoupling of Boolean control networks , 2013, Autom..

[34]  Jing Wang,et al.  Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback , 2018, Appl. Math. Comput..

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

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

[37]  Zhen Wang,et al.  Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems , 2012, Appl. Math. Comput..

[38]  Ranadip Pal,et al.  Context-Sensitive Probabilistic Boolean Networks: Steady-State Properties, Reduction, and Steady-State Approximation , 2010, IEEE Transactions on Signal Processing.

[39]  Jianquan Lu,et al.  Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks , 2014 .

[40]  L. Hood,et al.  A Genomic Regulatory Network for Development , 2002, Science.

[41]  Jinde Cao,et al.  Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy , 2012, IEEE Transactions on Neural Networks and Learning Systems.

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

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

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

[45]  Bo Gao,et al.  State analysis of Boolean control networks with impulsive and uncertain disturbances , 2017, Appl. Math. Comput..

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

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

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

[49]  Corrado Possieri,et al.  Observer design for Boolean control networks with unknown inputs , 2017 .

[50]  Jinde Cao,et al.  Function perturbations on singular Boolean networks , 2017, Autom..

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

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

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

[54]  Junwei Lu,et al.  Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays , 2018, Appl. Math. Comput..