Input-output decoupling control design for switched Boolean control networks

Abstract We investigate the input–output decoupling problem of switched Boolean control networks (SBCNs) in this paper. Based on the matrix expression of Boolean functions, the dynamics of SBCNs are converted into an algebraic form via semi-tensor product of matrices first. Then, using the redundant variable separation technique, we give the necessary and sufficient conditions for the existence of three kinds of controllers to detect whether an SBCN can be input–output decomposed or not, respectively, including the open-loop controllers, the state feedback controllers, and the output feedback controllers. Meanwhile, a constructive procedure is presented to construct the open-loop controllers, as well as the state feedback controllers and output feedback controllers. Finally, an illustrative example is given to show that the new results obtained are effective.

[1]  Yuzhen Wang,et al.  Output tracking of switched Boolean networks under open-loop/closed-loop switching signals☆ , 2016 .

[2]  Daizhan Cheng,et al.  Morgan’s problem of Boolean control networks , 2017 .

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

[4]  W. Respondek,et al.  On decomposition of nonlinear control systems , 1982 .

[5]  Yuzhen Wang,et al.  Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method , 2013, Autom..

[6]  Daizhan Cheng,et al.  Disturbance decoupling control design for switched Boolean control networks , 2014, Syst. Control. Lett..

[7]  Qiqi Yang,et al.  Pinning control design for robust output tracking of k-valued logical networks , 2017, J. Frankl. Inst..

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

[9]  Biao Wang,et al.  Matrix approach to model matching of composite asynchronous sequential machines , 2017 .

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

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

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

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

[14]  Maria Elena Valcher,et al.  Input/output decoupling of Boolean control networks , 2017 .

[15]  Yuzhen Wang,et al.  Formulation and optimization control of a class of networked evolutionary games with switched topologies , 2016 .

[16]  Daizhan Cheng,et al.  Optimal Control of Logical Control Networks , 2011, IEEE Transactions on Automatic Control.

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

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

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

[20]  F. Alsaadi,et al.  Semi-tensor product method to a class of event-triggered control for finite evolutionary networked games , 2017 .

[21]  L. Wang,et al.  Oscillations and chaos in neural networks: an exactly solvable model. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Daizhan Cheng,et al.  Identification of Boolean control networks , 2011, Autom..

[23]  Daizhan Cheng,et al.  Modeling, Analysis and Control of Networked Evolutionary Games , 2015, IEEE Transactions on Automatic Control.

[24]  Shihua Fu,et al.  A Matrix Approach to the Analysis and Control of Networked Evolutionary Games with Bankruptcy Mechanism , 2017 .

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

[26]  Yang Liu,et al.  Disturbance Decoupling of Singular Boolean Control Networks , 2016, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

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

[28]  Yang Liu,et al.  Event-Triggered Control for the Disturbance Decoupling Problem of Boolean Control Networks , 2018, IEEE Transactions on Cybernetics.

[29]  James Lam,et al.  Stability and Guaranteed Cost Analysis of Time-Triggered Boolean Networks , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[30]  Daniel W. C. Ho,et al.  Switching-signal-triggered pinning control for output tracking of switched Boolean networks , 2017 .

[31]  Daizhan Cheng,et al.  From weighted potential game to weighted harmonic game , 2017 .

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

[33]  Qing Zhang,et al.  Calculation of Siphons and Minimal Siphons in Petri Nets Based on Semi-Tensor Product of Matrices , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[34]  James Lam,et al.  l1-gain analysis and model reduction problem for Boolean control networks , 2016, Inf. Sci..

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

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

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

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

[39]  Jr. B. Morgan.  The synthesis of linear multivariable systems by state-variable feedback , 1964 .

[40]  Jitao Sun,et al.  Output controllability and optimal output control of state-dependent switched Boolean control networks , 2014, Autom..