Variable structure controller design for Boolean networks

The paper investigates the variable structure control for stabilization of Boolean networks (BNs). The design of variable structure control consists of two steps: determine a switching condition and determine a control law. We first provide a method to choose states from the reaching mode. Using this method, we can guarantee that the number of nodes which should be controlled is minimized. According to the selected states, we determine the switching condition to guarantee that the time of global stabilization in the BN is the shortest. A control law is then determined to ensure that all selected states can enter into the sliding mode, such that any initial state can arrive in the steady-state mode. Some examples are provided to illustrate the theoretical results.

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

[2]  Yorgo Istefanopulos,et al.  A new variable structure PID-controller design for robot manipulators , 2005, IEEE Transactions on Control Systems Technology.

[3]  Stanislav V. Emelyanov,et al.  Variable-Structure Control Systems , 1995 .

[4]  Jinde Cao,et al.  Sampled-Data State Feedback Stabilization of Boolean Control Networks , 2016, Neural Computation.

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

[6]  Chih-Chiang Cheng,et al.  A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems , 2003, IEEE Trans. Autom. Control..

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

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

[9]  Jinde Cao,et al.  Synchronization in an Array of Output-Coupled Boolean Networks With Time Delay , 2014, IEEE Transactions on Neural Networks and Learning Systems.

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

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

[12]  Jinde Cao,et al.  Synchronization Analysis of Master-Slave Probabilistic Boolean Networks , 2015, Scientific Reports.

[13]  Hong Liu,et al.  Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update , 2014, Scientific Reports.

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

[15]  Yuzhen Wang,et al.  Controllability Analysis and Control Design for Switched Boolean Networks with State and Input Constraints , 2015, SIAM J. Control. Optim..

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

[17]  Lihua Xie,et al.  Output tracking control of Boolean control networks via state feedback: Constant reference signal case , 2015, Autom..

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

[19]  Lihua Xie,et al.  On robust control invariance of Boolean control networks , 2016, at - Automatisierungstechnik.

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

[21]  Yuzhen Wang,et al.  Consistent stabilizability of switched Boolean networks , 2013, Neural Networks.

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

[23]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

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

[25]  Chen Hao,et al.  A new approach for global controllability of higher order Boolean control network , 2012, Proceedings of the 31st Chinese Control Conference.

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

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

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

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

[30]  H. De Battista,et al.  Dynamical variable structure controller for power regulation of wind energy conversion systems , 2004, IEEE Transactions on Energy Conversion.

[31]  Chung Choo Chung,et al.  Microstepping Using a Disturbance Observer and a Variable Structure Controller for Permanent-Magnet Stepper Motors , 2013, IEEE Transactions on Industrial Electronics.

[32]  Jinde Cao,et al.  On Controllability of Delayed Boolean Control Networks , 2016, SIAM J. Control. Optim..

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

[34]  Yuzhen Wang,et al.  Logical Matrix Factorization With Application to Topological Structure Analysis of Boolean Network , 2015, IEEE Transactions on Automatic Control.

[35]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[36]  Yang Liu,et al.  Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems , 2017 .

[37]  Fangfei Li,et al.  Complete synchronization of temporal Boolean networks , 2013, Neural Networks.

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

[39]  Zidong Wang,et al.  Pinning controllability of autonomous Boolean control networks , 2016, Science China Information Sciences.

[40]  Guodong Zhao,et al.  A survey on applications of semi-tensor product method in engineering , 2017, Science China Information Sciences.

[41]  Guanrong Chen,et al.  A fuzzy adaptive variable structure controller with applications to robot manipulators , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[42]  Jinde Cao,et al.  Synchronization in output-coupled temporal Boolean networks , 2014, Scientific Reports.

[43]  Satoru Miyano,et al.  Identification of Genetic Networks from a Small Number of Gene Expression Patterns Under the Boolean Network Model , 1998, Pacific Symposium on Biocomputing.