logo

SCIENCE CHINA Information Sciences, Volume 60, Issue 2: 022202(2017) https://doi.org/10.1007/s11432-015-0611-4

Output reachability analysis and output regulation control design of Boolean control networks

More info
  • ReceivedMar 12, 2016
  • AcceptedMay 12, 2016
  • PublishedDec 15, 2016

Abstract

This paper investigates the output reachability and output regulation control design of Boolean control networks (BCNs) by using the semi-tensor product method, and presents a number of new results. First, the concept of output reachability is proposed for BCNs, and some necessary and sufficient conditions are presented for the verification of output reachability. Second, based on the output reachability of BCNs and the attractor set of the reference Boolean network, an effective method is proposed for the control design of the output regulation problem. The study of an illustrative example shows the effectiveness of the obtained new results.


Funded by

National Natural Science Foundation of China(61374065)

National Natural Science Foundation of China(61503225)

Natural Science Foundation of Shandong Province(ZR2015FQ003)


Acknowledgment

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. 61374065, 61503225), Natural Science Foundation of Shandong Province (Grant No. ZR2015FQ003), and Research Fund for the Taishan Scholar Project of Shandong Province.


References

[1] Francis B A. The linear multivariable regulator problem. SIAM J Contr Optim, 1977, 15: 486-505 CrossRef Google Scholar

[2] Huang J, Chen Z. A general framework for tackling the output regulation problem. IEEE Trans Automat Control, 2004, 49: 2203-2218 CrossRef Google Scholar

[3] Isidori A, Byrnes C I. Output regulation of nonlinear systems. IEEE Trans Automat Control, 1990, 35: 131-140 CrossRef Google Scholar

[4] Julius A A, Halasz A, Sakar M S, et al. Stochastic modeling and control of biological systems: the lactose regulation system of Escherichia coli. IEEE Trans Automat Control, 2008, 53: 51-65 CrossRef Google Scholar

[5] Akutsu T, Hayashida M, Ching W, et al. Control of Boolean networks: hardness results and algorithms for tree structured networks. J Theor Biol, 2007, 244: 670-679 CrossRef Google Scholar

[6] Cheng D Z, Qi H S, Li Z Q. Analysis and Control of Boolean Networks: a semi-tensor Product Approach. London: Springer-Verlag, 2011. Google Scholar

[7] Cheng D Z, Qi H S, Zhao Y. An Introduction to Semi-tensor Product of Matrices and Its Applications. Singapore: World Scientific, 2012. Google Scholar

[8] Cheng D Z, Qi H S. A linear representation of dynamics of Boolean networks. IEEE Trans Automat Control, 2010, 55: 2251-2258 CrossRef Google Scholar

[9] Cheng D Z, Qi H S. Controllability and observability of Boolean control networks. Automatica, 2009, 45: 1659-1667 CrossRef Google Scholar

[10] Zhang L J, Zhang K Z. Controllability and observability of Boolean control networks with time-variant delays in states. IEEE Trans Neural Netw Learn Syst, 2013, 24: 1478-1484 CrossRef Google Scholar

[11] Li Z Q, Song J L. Controllability of Boolean control networks avoiding states set. Sci China Inf Sci, 2014, 57: 032205-1484 Google Scholar

[12] Chen H, Sun J. Output controllability and optimal output control of state-dependent switched Boolean control networks. Automatica, 2014, 50: 1929-1934 CrossRef Google Scholar

[13] Guo Y Q. Controllability of Boolean control networks with state-dependent constraints. Sci China Inf Sci, 2016, 59: 032202-1934 CrossRef Google Scholar

[14] Li F F, Sun J T. Controllability of probabilistic Boolean control networks. Automatica, 2011, 47: 2765-2771 CrossRef Google Scholar

[15] Li R, Yang M, Chu T G. State feedback stabilization for Boolean control networks. IEEE Trans Automat Control, 2013, 58: 1853-1857 CrossRef Google Scholar

[16] Zhao Y, Cheng D Z. On controllability and stabilizability of probabilistic Boolean control networks. Sci China Inf Sci, 2014, 57: 012202-1857 Google Scholar

[17] Yang M, Li R, Chu T G. Controller design for disturbance decoupling of Boolean control networks. Automatica, 2013, 49: 273-277 CrossRef Google Scholar

[18] Laschov D, Margaliot M. Minimum-time control of Boolean networks. SIAM J Contr Optim, 2013, 51: 2869-2892 CrossRef Google Scholar

[19] Zhao Y, Li Z Q, Cheng D Z. Optimal control of logical control network. IEEE Trans Automat Control, 2011, 56: 1766-1776 CrossRef Google Scholar

[20] Liu Z B, Wang Y Z, Li H T. Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks. Sci China Inf Sci, 2014, 57: 052201-1776 Google Scholar

[21] Zou Y L, Zhu J D. System decomposition with respect to inputs for Boolean control networks. Automatica, 2014, 50: 1304-1309 CrossRef Google Scholar

[22] Xu X R, Hong Y G. Matrix approach to model matching of asynchronous sequential machines. IEEE Trans Automat Control, 2013, 58: 2974-2979 CrossRef Google Scholar

[23] Feng J E, Yao J, Cui P. Singular Boolean networks: Semi-tensor product approach. Sci China Inf Sci, 2013, 56: 112203-2979 Google Scholar

[24] Wang Y Z, Zhang C H, Liu Z B. A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems. Automatica, 2012, 48: 1227-1236 CrossRef Google Scholar

[25] Guo P L, Wang Y Z, Li H T. Stable degree analysis for strategy profiles of evolutionary networked games. Sci China Inf Sci, 2016, 59: 052204-1236 CrossRef Google Scholar

[26] Zhao D W, Peng H P, Li L X, et al. Novel way to research nonlinear feedback shift register. Sci China Inf Sci, 2014, 57: 092114-1236 Google Scholar

[27] Zhong J H, Lin D D. Stability of nonlinear feedback shift registers. Sci China Inf Sci, 2016, 59: 012204-1236 Google Scholar

[28] Zhong J, Lu J Q, Liu Y, et al. Synchronization in an array of output-coupled Boolean networks with time delay. IEEE Trans Neural Netw Learn Syst, 2014, 25: 2288-2294 CrossRef Google Scholar

[29] Cheng D Z. On finite potential games. Automatica, 2014, 50: 1793-1801 CrossRef Google Scholar

[30] Cheng D Z, He F, Qi H, et al. Modeling, analysis and control of networked evolutionary games. IEEE Trans Automat Control, 2015, 60: 2402-2415 CrossRef Google Scholar

[31] Fornasini E, Valcher M. Feedback stabilization, regulation and optimal control of Boolean control networks. In: Proceedings of 2014 American Control Conference, Portland, 2014. 1981--1986. Google Scholar

[32] Li H T, Wang Y Z, Xie L H. Output tracking control of Boolean control networks via state feedback: constant reference signal case. Automatica, 2015, 59: 54-59 CrossRef Google Scholar

[33] Li H T, Wang Y Z, Guo P L. Solvability of state feedback based output regulation for Boolean control networks. In: Proceedings of the 34th Chinese Control Conference, Hangzhou, 2015. 401--406. Google Scholar

[34] Zhao Y, Cheng D Z, Qi H S. Input-state incidence matrix of Boolean control networks and its applications. Syst Contr Lett, 2010, 59: 767-774 CrossRef Google Scholar

Copyright 2019 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1