Input observability of Boolean control networks

Abstract This paper devotes to the input observability, which also is called the nonsingularity or left invertibility, of general Boolean control networks. First, using graphic approach converts the global nonsingularity into pointwise finite-step nonsingularity. Subsequently, a series of matrix-form criterions are given to identify the nonsingularity, under which suitable inverse Boolean control networks can be designed. Finally, one application and one numerical example are used to illustrate the feasibility and validity of the obtained results.

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

[2]  Kuize Zhang On nonsingularity of Boolean control networks , 2016, 2016 American Control Conference (ACC).

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

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

[5]  Fuad E. Alsaadi,et al.  Set stabilization of Boolean networks under pinning control strategy , 2017, Neurocomputing.

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

[7]  R. Brockett,et al.  The reproducibility of multivariable systems , 1964 .

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

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

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

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

[12]  Daizhan Cheng,et al.  A note on observability of Boolean control networks , 2015, 2015 10th Asian Control Conference (ASCC).

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

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

[15]  P. Moylan Stable inversion of linear systems , 1977 .

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

[17]  Bernard Widrow,et al.  Adaptive Inverse Control: A Signal Processing Approach , 2007 .

[18]  Lijun Zhang,et al.  An Application of Invertibility of Boolean Control Networks to the Control of the Mammalian Cell Cycle , 2017, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

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

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

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

[22]  Jun‐e Feng,et al.  Stabilizability analysis and switching signals design of switched Boolean networks , 2018, Nonlinear Analysis: Hybrid Systems.

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

[24]  Jinling Liang,et al.  Output regulation of Boolean control networks with stochastic disturbances , 2017 .

[25]  Pan Wang,et al.  Set stability and set stabilization of Boolean control networks based on invariant subsets , 2015, Autom..

[26]  Ben M. Chen,et al.  Linear Systems Theory: A Structural Decomposition Approach , 2004 .

[27]  J. Massey,et al.  Invertibility of linear time-invariant dynamical systems , 1969 .

[28]  H. Othmer,et al.  The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. , 2003, Journal of theoretical biology.

[29]  Fangfei Li,et al.  Global stability at a limit cycle of switched Boolean networks under arbitrary switching signals , 2014, Neurocomputing.

[30]  Guodong Zhao,et al.  Invertibility of higher order k-valued logical control networks and its application in trajectory control , 2016, J. Frankl. Inst..

[31]  Gregory L. Plett,et al.  Adaptive inverse control of linear and nonlinear systems using dynamic neural networks , 2003, IEEE Trans. Neural Networks.

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