Search Advanced

AIMS Mathematics

2022, Volume 7, Issue 6: 9668-9682. doi: 10.3934/math.2022538
Previous Article Next Article
Research article Special Issues

Trajectory tracking approach to logical (control) networks

  • 1.
    School of Mathematics, Shandong University, Jinan, Shandong 250100, China
  • 2.
    Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, China
  • 3.
    Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng University, Liaocheng 252000, China
  • 4.
    School of Mathematical Science, Liaocheng University, Liaocheng 252000, China
  • Received: 23 December 2021 Revised: 23 February 2022 Accepted: 01 March 2022 Published: 15 March 2022

  • MSC : 93-XX

  • Vector form expression of logical (control) networks is presented. From this aspect, the trajectory table is proposed to investigate Boolean networks. Based on it, the topology structure, controllability and observability of logical (control) networks are analyzed. Compared to the method of logical matrix, vector form expression called structure vector method decreases the computational complex. Numerical examples show that the complexity of the structure vector method is greatly reduced.

    Citation: Xiaoyu Zhao, Shihua Fu. Trajectory tracking approach to logical (control) networks[J]. AIMS Mathematics, 2022, 7(6): 9668-9682. doi: 10.3934/math.2022538

    Related Papers:

  • Vector form expression of logical (control) networks is presented. From this aspect, the trajectory table is proposed to investigate Boolean networks. Based on it, the topology structure, controllability and observability of logical (control) networks are analyzed. Compared to the method of logical matrix, vector form expression called structure vector method decreases the computational complex. Numerical examples show that the complexity of the structure vector method is greatly reduced.


    加载中


    [1] S. A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theor. Biol., 22 (1969), 437–467. https://doi.org/10.1016/0022-5193(69)90015-0 doi: 10.1016/0022-5193(69)90015-0
    [2] S. Wang, J. E. Feng, Y. Yu, J. Zhao, Further results on dynamic-algebraic Boolean control networks, Sci. China Inform. Sci., 62 (2019), 1–14. https://doi.org/10.1007/s11432-018-9447-4 doi: 10.1007/s11432-018-9447-4
    [3] D. Cheng, H. Qi, Controllability and observability of Boolean control networks, Automatica, 45 (2009), 1659–1667. https://doi.org/10.1016/j.automatica.2009.03.006 doi: 10.1016/j.automatica.2009.03.006
    [4] D. Cheng, Input-state approach to Boolean networks, IEEE T. Neural Networ., 20 (2009), 512–521. https://doi.org/10.1109/TNN.2008.2011359 doi: 10.1109/TNN.2008.2011359
    [5] D. Cheng, H. Qi, Z. Li, Analysis and control of Boolean networks: A semi-tensor product approach, London: Springer, 2011.
    [6] J. Zhong, D. W. C. Ho, J. Lu, A new approach to pinning control of Boolean networks, IEEE T. Control Netw., 2021. https://doi.org/10.1109/TCNS.2021.3106453
    [7] M. R. Rafimanzelat, F. Bahrami, Attactor controllability of Boolean networks by fipping a subset of their nodes, Chaos, 28 (2018), 043120. https://doi.org/10.1063/1.4999950 doi: 10.1063/1.4999950
    [8] F. Li, Y. Tang, Pinning controllability for a Boolean network with arbitrary disturbance inputs, IEEE T. Cybernetics, 51 (2021), 3338–3347. https://doi.org/10.1109/TCYB.2019.2930734 doi: 10.1109/TCYB.2019.2930734
    [9] Y. Yu, M. Meng, J. Feng, G. Chen, Observability criteria for Boolean networks, IEEE T. Automat. Contr., 2021. https://doi.org/10.1109/TAC.2021.3131436
    [10] Y. Yu, M. Meng, J. Feng, Observability of Boolean networks via matrix equations, Automatica, 111 (2020), 108621. https://doi.org/10.1016/j.automatica.2019.108621 doi: 10.1016/j.automatica.2019.108621
    [11] J. Yang, W. Qian, Z. Li, Redefined reconstructibility and state estimation for Boolean networks, IEEE T. Control Netw., 7 (2020), 1882–1890. https://doi.org/10.1109/TCNS.2020.3007820 doi: 10.1109/TCNS.2020.3007820
    [12] H. Li, X. Yang, S. Wang, Robustness for stability and stabilization of Boolean networks with stochastic function perturbations, IEEE T. Automat. Contr., 66 (2021), 1231–1237. https://doi.org/10.1109/TAC.2020.2997282 doi: 10.1109/TAC.2020.2997282
    [13] Q. Zhang, J. Feng, Y. Zhao, J. Zhao, Stabilization and set stabilization of switched Boolean control networks via flipping mechanism, Nonlinear Anal.: Hybrid Syst., 41 (2021), 101055. https://doi.org/10.1016/j.nahs.2021.101055 doi: 10.1016/j.nahs.2021.101055
    [14] B. Chen, X. Yang, Y. Liu, J. Liu, Controllability and stabilization of Boolean control networks by the auxiliary function of flipping, Int. J. Robust Nonlinear Control, 30 (2020), 5529–5541. https://doi.org/10.1002/rnc.5091 doi: 10.1002/rnc.5091
    [15] Y. Wang, P. Guo, Optimal control of singular Boolean control networks via Ledley solution method, J. Franklin Inst., 358 (2021), 6161–6173. https://doi.org/10.1016/j.jfranklin.2021.06.006 doi: 10.1016/j.jfranklin.2021.06.006
    [16] X. Ding, H. Li, Optimal control of random evolutionary Boolean games, Int. J. Control, 94 (2021), 144–152. https://doi.org/10.1080/00207179.2019.1585957 doi: 10.1080/00207179.2019.1585957
    [17] Y. Zheng, J. Feng, Output tracking of delayed logical control networks with multi-constraints, Front. Inform. Technol. Electron. Eng., 21 (2020), 316–323. https://doi.org/10.1631/FITEE.1900376 doi: 10.1631/FITEE.1900376
    [18] Q. Zhang, J. Feng, T. Jiao, Finite horizon tracking control of probabilistic Boolean control networks, J. Franklin Inst., 358 (2021), 9909–9928. https://doi.org/10.1016/j.jfranklin.2021.10.003 doi: 10.1016/j.jfranklin.2021.10.003
    [19] Y. Li, J. Zhu, B. Li, Y. Liu, J. Lu, A necessary and sufficient graphic condition for the original disturbance decoupling of Boolean networks, IEEE T. Automat. Contr., 66 (2021), 3765–3772. https://doi.org/10.1109/TAC.2020.3025507 doi: 10.1109/TAC.2020.3025507
    [20] Y. Yu, J. Feng, J. Pan, D. Cheng, Block decoupling of Boolean control networks, IEEE T. Automat. Contr., 64 (2019), 3129–3140. https://doi.org/10.1109/TAC.2018.2880411 doi: 10.1109/TAC.2018.2880411
    [21] M. Meng, J. Feng, Z. Hou, Synchronization of interconnected multi-valued logical networks, Asian J. Control, 16 (2014), 1659–1669. https://doi.org/10.1002/asjc.835 doi: 10.1002/asjc.835
    [22] Y. Li, J. Feng, S. Zhu, Controllability and reachability of periodically time-variant mixed-valued logical control networks, Circuits, Syst., Signal Process., 40 (2021), 3639–3654. https://doi.org/10.1007/s00034-021-01648-2 doi: 10.1007/s00034-021-01648-2
    [23] Y. Li, H. Li, X. Ding, Set stability of switched delayed logical networks with application to finite-field consensus, Automatica, 113 (2021), 108768. https://doi.org/10.1016/j.automatica.2019.108768 doi: 10.1016/j.automatica.2019.108768
    [24] Y. Wu, S. Le, K. Zhang, X. Sun, Ex-ante agent transformation of Bayesian games, IEEE T. Automat. Contr., 2021. https://doi.org/10.1109/TAC.2021.3122372
    [25] H. Qi, B. Mu, I. R. Petersen, G. Shi, Measurement-induced Boolean dynamics and controllability for closed quantum networks, Automatica, 114 (2020), 108816. https://doi.org/10.1016/j.automatica.2020.108816 doi: 10.1016/j.automatica.2020.108816
    [26] J. Zhong, D. Lin, Decomposition of nonlinear feedback shift registers based on Boolean networks, Sci.China Inform. Sci., 62 (2019), 1–3. https://doi.org/10.1007/s11432-017-9460-4 doi: 10.1007/s11432-017-9460-4
    [27] J. Lu, B. Li, J. Zhong, A novel synthesis method for reliable feedback shift registers via Boolean networks, Sci. China Inform. Sci., 64 (2021), 1–14. https://doi.org/10.1007/s11432-020-2981-4 doi: 10.1007/s11432-020-2981-4
    [28] X. Xu, Y. Hong, Observability analysis and observer design for finite automata via matrix approach, IET Control Theory Appl., 7 (2013), 1609–1615.
    [29] X. Han, Z. Chen, Z. Liu, Q. Zhang, Calculation of siphons and minimal siphons in petri nets based on semi-tensor product of matrices, IEEE T. Syst., Man, Cybern.: Syst., 47 (2017), 531–536. https://doi.org/10.1109/TSMC.2015.2507162 doi: 10.1109/TSMC.2015.2507162
    [30] H. Lyu, W. Wang, X. Liu, Universal approximation of multi-variable fuzzy systems by semi-tensor product, IEEE T. Fuzzy Syst., 28 (2020), 2972–2981.
    [31] D. Cheng, Y. Li, J. Feng, J. Zhao, On numerical/non-numerical algebra: Semi-tensor product method, Math. Model. Control, 1 (2021), 1–11. https://doi.org/10.3934/mmc.2021001 doi: 10.3934/mmc.2021001
    [32] S. Fu, D. Cheng, J. Feng, J. Zhao, Matrix expression of finite Boolean-type algebras, Appl. Math. Comput., 395 (2021), 125880. https://doi.org/10.1016/j.amc.2020.125880 doi: 10.1016/j.amc.2020.125880
    [33] Z. Liu, J. Zhong, Y. Liu, W. Gui, Weak stabilization of Boolean networks under state-flipped control, IEEE T. Neural Netw. Learn. Syst., 2021. https://doi.org/10.1109/TNNLS.2021.3106918
    [34] A. Acernese, A. Yerudkar, L. Glielmo, C. Del Vecchio, Model-free self-triggered control co-design for probabilistic Boolean control networks, IEEE Control Syst. Lett., 5 (2021), 1639–1644. https://doi.org/10.1109/LCSYS.2020.3042394 doi: 10.1109/LCSYS.2020.3042394
    [35] A. Acernese, A. Yerudkar, L. Glielmo, C. Del Vecchio, Double deep-Q learning-based output tracking of probabilistic Boolean control networks, IEEE Access, 8 (2020), 199254–199265. https://doi.org/10.1109/ACCESS.2020.3035152 doi: 10.1109/ACCESS.2020.3035152
    [36] D. Cheng, H. Qi, Y. Zhao, An introduction to semi-tensor product of matrices and its applications, Singapore: World Scientific, 2012.
    [37] R. Gibbons, A primer in game theory, New York: Printice Hall, 1992.
    [38] D. Cheng, C. Li, F. He, Observability of Boolean networks via set controllability, Syst. Control Lett., 115 (2018), 22–25. https://doi.org/10.1016/j.sysconle.2018.03.004 doi: 10.1016/j.sysconle.2018.03.004
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(1621) PDF downloads(128) Cited by(2)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(6)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog