Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

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

布尔控制网络的输出能达分析与输出调节控制设计

  • 120 Accesses

  • 15 Citations

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.

创新点

本文利用矩阵半张量积方法研究了布尔控制网络的输出能达分析与输出调节控制设计问题。本文的主要创新点为: (1)利用矩阵半张量积方法建立了布尔控制网络输出能达的若干充分必要条件, 这些条件为布尔控制网络的输出调节控制设计奠定了基础。 (2)基于输出能达和参考系统的极限集, 建立了布尔控制网络状态反馈输出调节控制器的设计方法, 即极限集驱动方法。 (3)本文建立的方法, 能够有效处理时变参考信号, 从而为布尔控制网络的其它输出控制问题提供了可借鉴的方法。

This is a preview of subscription content, log in to check access.

References

  1. 1

    Francis B A. The linear multivariable regulator problem. SIAM J Contr Optim, 1977, 15: 486–505

  2. 2

    Huang J, Chen Z. A general framework for tackling the output regulation problem. IEEE Trans Automat Control, 2004, 49: 2203–2218

  3. 3

    Isidori A, Byrnes C I. Output regulation of nonlinear systems. IEEE Trans Automat Control, 1990, 35: 131–140

  4. 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

  5. 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

  6. 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

  7. 7

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

  8. 8

    Cheng D Z, Qi H S. A linear representation of dynamics of Boolean networks. IEEE Trans Automat Control, 2010, 55: 2251–2258

  9. 9

    Cheng D Z, Qi H S. Controllability and observability of Boolean control networks. Automatica, 2009, 45: 1659–1667

  10. 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

  11. 11

    Li Z Q, Song J L. Controllability of Boolean control networks avoiding states set. Sci China Inf Sci, 2014, 57: 032205

  12. 12

    Chen H, Sun J. Output controllability and optimal output control of state-dependent switched Boolean control networks. Automatica, 2014, 50: 1929–1934

  13. 13

    Guo Y Q. Controllability of Boolean control networks with state-dependent constraints. Sci China Inf Sci, 2016, 59: 032202

  14. 14

    Li F F, Sun J T. Controllability of probabilistic Boolean control networks. Automatica, 2011, 47: 2765–2771

  15. 15

    Li R, Yang M, Chu T G. State feedback stabilization for Boolean control networks. IEEE Trans Automat Control, 2013, 58: 1853–1857

  16. 16

    Zhao Y, Cheng D Z. On controllability and stabilizability of probabilistic Boolean control networks. Sci China Inf Sci, 2014, 57: 012202

  17. 17

    Yang M, Li R, Chu T G. Controller design for disturbance decoupling of Boolean control networks. Automatica, 2013, 49: 273–277

  18. 18

    Laschov D, Margaliot M. Minimum-time control of Boolean networks. SIAM J Contr Optim, 2013, 51: 2869–2892

  19. 19

    Zhao Y, Li Z Q, Cheng D Z. Optimal control of logical control network. IEEE Trans Automat Control, 2011, 56: 1766–1776

  20. 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

  21. 21

    Zou Y L, Zhu J D. System decomposition with respect to inputs for Boolean control networks. Automatica, 2014, 50: 1304–1309

  22. 22

    Xu X R, Hong Y G. Matrix approach to model matching of asynchronous sequential machines. IEEE Trans Automat Control, 2013, 58: 2974–2979

  23. 23

    Feng J E, Yao J, Cui P. Singular Boolean networks: Semi-tensor product approach. Sci China Inf Sci, 2013, 56: 112203

  24. 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

  25. 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

  26. 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

  27. 27

    Zhong J H, Lin D D. Stability of nonlinear feedback shift registers. Sci China Inf Sci, 2016, 59: 012204

  28. 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

  29. 29

    Cheng D Z. On finite potential games. Automatica, 2014, 50: 1793–1801

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

Download references

Acknowledgements

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.

Author information

Correspondence to Haitao Li.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, H., Wang, Y. & Guo, P. Output reachability analysis and output regulation control design of Boolean control networks. Sci. China Inf. Sci. 60, 022202 (2017). https://doi.org/10.1007/s11432-015-0611-4

Download citation

Keywords

  • Boolean control network
  • output reachability
  • output regulation
  • control design
  • semi-tensor prod- uct of matrices

关键词

  • 布尔控制网络
  • 输出能达
  • 输出调节
  • 控制设计
  • 矩阵半张量积