Controllability and Optimal Control of Higher-Order Incomplete Boolean Control Networks With Impulsive Effects

This paper investigates the controllability and optimal control of higher order incomplete Boolean control networks (BCNs) with impulsive effects by using the semi-tensor product of matrices. First, the incomplete logical system is expressed as an algebraic form, based on which several necessary and sufficient conditions for the controllability are presented. Then, the Mayer-type optimal control issue is studied and the optimal control design algorithms are established. At last, the study of illustrative examples shows the effectiveness of the obtained new results.

[1]  W. Marsden.  I and J , 2012 .

[2]  James Lam,et al.  An Improved Criterion for Controllability of Boolean Control Networks , 2017, IEEE Transactions on Automatic Control.

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

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

[5]  Daizhan Cheng,et al.  Incomplete Logical Control System and its Application to Some Intellectual Problems , 2018 .

[6]  Michael Margaliot,et al.  Minimal Controllability of Conjunctive Boolean Networks is NP-Complete , 2017, Autom..

[7]  Yong Ding,et al.  Time-optimal state feedback stabilization of switched Boolean control networks , 2017, Neurocomputing.

[8]  Jitao Sun,et al.  A new approach for global controllability of higher order Boolean control network , 2013, Neural Networks.

[9]  Jitao Sun,et al.  On hybrid control of higher order Boolean networks , 2014, Neurocomputing.

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

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

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

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

[14]  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.

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

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

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

[18]  Mohsen Montazeri,et al.  Controllability and stabilizability of multi-rate sampled data systems , 2018, Syst. Control. Lett..

[19]  Jun‐e Feng,et al.  Topological structure and optimal control of singular mix-valued logical networks , 2015 .

[20]  Jiandong Zhu,et al.  Reachability of higher-order logical control networks via matrix method , 2016, Appl. Math. Comput..

[21]  Guodong Zhao,et al.  Modelling and strategy optimisation for a kind of networked evolutionary games with memories under the bankruptcy mechanism , 2018, Int. J. Control.

[22]  Daizhan Cheng,et al.  Analysis and Control of Boolean Networks , 2011 .

[23]  Weiwei Sun,et al.  Event-triggered control for robust set stabilization of logical control networks , 2018, Autom..

[24]  James Lam,et al.  Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances , 2008, IEEE Transactions on Automatic Control.

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

[26]  Zhong-Ping Jiang,et al.  Stochastic and adaptive optimal control of uncertain interconnected systems: A data-driven approach , 2018, Syst. Control. Lett..

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

[28]  Luis G. Vargas,et al.  An optimization-based approach for the design of Bayesian networks , 2008, Math. Comput. Model..

[29]  Daniel W. C. Ho,et al.  Global robust stability and stabilization of Boolean network with disturbances , 2017, Autom..

[30]  Fangfei Li,et al.  Robust Stabilization for a Logical System , 2017, IEEE Transactions on Control Systems Technology.

[31]  Yuzhen Wang,et al.  Disturbance decoupling of mix-valued logical networks via the semi-tensor product method , 2012, Autom..

[32]  M. Ng,et al.  Control of Boolean networks: hardness results and algorithms for tree structured networks. , 2007, Journal of theoretical biology.

[33]  Neil Genzlinger.  A. and Q , 2006 .