Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems

Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This study presents a detailed survey on recent development of logical networks and its applications, including the background of logical networks, the theory of a new matrix product called semi-tensor product (STP) of matrices, some fundamental works on logical networks, and some current research works. Particularly, some fundamental works on logical networks are presented for the past years, including controllability, stability and stabilisation, synchronisation, disturbance decoupling and so on. Due to the great potential of STP in dealing with logical networks, a surge of attraction from overseas is paid on the study of STP and its applications. Currently, some new research areas are widely studied including pinning control, function perturbations, system decomposition, trajectory control, output tracking issues, symbolic dynamics and so on. The main concern of this study is to present a comprehensive introduction to logical networks and some other applications under the framework of STP of matrices.

References

    1. 1)
      • 1. Kauffman, S.A.: ‘Metabolic stability and epigenesis in randomly constructed genetic nets’, J. Theor. Biol., 1969, 22, (3), pp. 437467.
    2. 2)
      • 116. Wu, Y., Shen, T.: ‘A logical dynamical systems approach to modeling and control of residual gas fraction in IC engines’, IFAC Proc., 2013, 46, (21), pp. 495500.
    3. 3)
      • 104. Rushdi, A., Ghaleb, F.: ‘A tutorial exposition of semi-tensor products of matrices with a stress on their representation of Boolean functions’, J. King Abdulaziz Univ. FCIT, 2013.
    4. 4)
      • 60. 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, (4), pp. 670679.
    5. 5)
      • 72. Zhong, J., Lu, J., Huang, T., et al: ‘Controllability and synchronization analysis of identical-hierarchy mixed-valued logical control networks’, IEEE Trans. Cybern., 2016, pp. 112, doi: 10.1109/TCYB.2016.2560240.
    6. 6)
      • 50. Zou, Y., Zhu, J.: ‘System decomposition with respect to inputs for Boolean control networks’, Automatica, 2014, 50, (4), pp. 13041309.
    7. 7)
      • 82. Cheng, D., Xu, T., Qi, H.: ‘Evolutionarily stable strategy of networked evolutionary games’, IEEE Trans. Neural Netw. Learn. Syst., 2014, 25, (7), pp. 13351345.
    8. 8)
      • 115. Laschov, D., Margaliot, M.: ‘Controllability of Boolean control networks via perron-frobenius theory’, Automatica, 2012, 48, (6), pp. 12181223.
    9. 9)
      • 88. Cheng, D., Qi, H., Liu, T., et al: ‘A note on observability of Boolean control networks’, Syst. Control Lett., 2016, 87, pp. 7682.
    10. 10)
      • 3. Li, H., Wang, Y.: ‘Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method’, Automatica, 2012, 48, (4), pp. 688693.
    11. 11)
      • 8. Cheng, D., Qi, H., Li, Z.: ‘Analysis and control of Boolean networks: a semi-tensor product approach’ (Springer Science & Business Media, 2010).
    12. 12)
      • 69. Zhang, L., Feng, J., Feng, X., et al: ‘Further results on disturbance decoupling of mix-valued logical networks’, IEEE Trans. Autom. Control, 2014, 59, (6), pp. 16301634.
    13. 13)
      • 48. Fornasini, E., Valcher, M.: ‘Fault detection analysis of Boolean control networks’, IEEE Trans. Autom. Control, 2015, 60, (10), pp. 27342739.
    14. 14)
      • 71. Liu, Z., Wang, Y., Li, H.: ‘Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks’, Sci. China Inform. Sci., 2014, 57, (5), pp. 110.
    15. 15)
      • 74. Cheng, D., Zhao, Y., Xu, T.: ‘Receding horizon based feedback optimization for mix-valued logical networks’, IEEE Trans. Autom. Control, 2015, 60, (12), pp. 33623366.
    16. 16)
      • 62. Zhao, Y., Ghosh, B.K., Cheng, D.: ‘Control of large-scale Boolean networks via network aggregation’, IEEE Trans. Neural Netw. Learn. Syst., 2016, 27, (7), pp. 15271536.
    17. 17)
      • 111. Xiao, Y., Dougherty, E.R.: ‘The impact of function perturbations in Boolean networks’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2007, 23, (10), pp. 12651273.
    18. 18)
      • 53. Laschov, D., Margaliot, M.: ‘A maximum principle for single-input Boolean control networks’, IEEE Trans. Autom. Control, 2011, 56, (4), pp. 913917.
    19. 19)
      • 25. Guo, Y., Wang, P., Gui, W., et al: ‘Set stability and set stabilization of Boolean control networks based on invariant subsets’, Automatica, 2015, 61, pp. 106112.
    20. 20)
      • 14. Li, F., Sun, J.: ‘Stability and stabilization of Boolean networks with impulsive effects’, Syst. Control Lett., 2012, 61, (1), pp. 15.
    21. 21)
      • 11. Lu, J., Zhong, J., Ho, D., et al: ‘On controllability of delayed Boolean control networks’, SIAM J. Control Optim., 2016, 54, (2), pp. 475494.
    22. 22)
      • 12. Liu, Y., Lu, J., Wu, B.: ‘Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks’, ESAIM Control Optim Calculus Variat., 2014, 20, (1), pp. 158173.
    23. 23)
      • 89. Li, R., Chu, T.: ‘Synchronization in an array of coupled Boolean networks’, Mod. Phys. Lett. A, 2012, 376, (45), pp. 30713075.
    24. 24)
      • 39. Liu, Y., Li, B., Lou, J.: ‘Disturbance decoupling of singular Boolean control networks’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2016, 13, pp. 11941200.
    25. 25)
      • 47. Li, H., Xie, L., Wang, Y.: ‘Output regulation of Boolean control networks’, IEEE Trans. Autom. Control, 2016, doi: 10.1109/TSMC.2015.2507162.
    26. 26)
      • 86. Khatri, C., Rao, C.: ‘Solutions to some functional equations and their applications to characterization of probability distributions’, Sankhyā, 1968, 30, (2), pp. 167180.
    27. 27)
      • 90. Zhong, J., Lu, J., Huang, T., et al: ‘Synchronization of master–slave Boolean networks with impulsive effects: necessary and sufficient criteria’, Neurocomputing, 2014, 143, pp. 269274.
    28. 28)
      • 70. Liu, Z., Wang, Y.: ‘Disturbance decoupling of mix-valued logical networks via the semi-tensor product method’, Automatica, 2012, 48, (8), pp. 18391844.
    29. 29)
      • 81. Zhao, G., Wang, Y.: ‘Formulation and optimization control of a class of networked evolutionary games with switched topologies’, Nonlinear Anal. Hybrid Syst., 2016, 22, pp. 98107.
    30. 30)
      • 58. Fornasini, E., Valcher, M.E.: ‘Recent developments in Boolean networks control’, J. Control Decis., 2016, 3, (1), pp. 118.
    31. 31)
      • 99. Li, F.: ‘Synchronization of coupled large-scale Boolean networks’, Chaos, 2014, 24, (1), p. 013115.
    32. 32)
      • 76. Wang, Y., Zhang, C., Liu, Z.: ‘A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems’, Bul. Inst. Politeh. ‘Gheorghe Gheorghiu-Dej’ Bucur. Ser. Autom., 2012, 48, (7), pp. 12271236.
    33. 33)
      • 64. Meng, M., Lam, J., Feng, J., et al: ‘l1-gain analysis and model reduction problem for Boolean control networks’, Inf. Sci., 2016, 348, pp. 6883.
    34. 34)
      • 107. Li, R., Yang, M., Chu, T.: ‘State feedback stabilization for probabilistic Boolean networks’, Automatica, 2014, 50, (4), pp. 12721278.
    35. 35)
      • 97. Li, F.: ‘Pinning control design for the synchronization of two coupled Boolean networks’, IEEE Trans. Circ. Syst. II Express Briefs, 2016, 63, (3), pp. 309313.
    36. 36)
      • 103. Bof, N., Fornasini, E., Valcher, M.E.: ‘Output feedback stabilization of Boolean control networks’, Automatica, 2015, 1, (2), pp. 139.
    37. 37)
      • 38. Li, H., Wang, Y., Xie, L., et al: ‘Disturbance decoupling control design for switched Boolean control networks’, Syst. Control Lett., 2014, 72, pp. 16.
    38. 38)
      • 63. Li, H., Wang, Y.: ‘Logical matrix factorization with application to topological structure analysis of Boolean network’, IEEE Trans. Autom. Control, 2015, 60, (5), pp. 13801385.
    39. 39)
      • 20. Fornasini, E., Valcher, M.E.: ‘On the periodic trajectories of Boolean control networks’, Automatica, 2013, 49, (5), pp. 15061509.
    40. 40)
      • 4. Cheng, D., Feng, J., Lv, H.: ‘Solving fuzzy relational equations via semitensor product’, IEEE Trans. Fuzzy Syst., 2012, 20, (2), pp. 390396.
    41. 41)
      • 106. Shmulevich, I., Dougherty, E.R., Zhang, W.: ‘Gene perturbation and intervention in probabilistic Boolean networks’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2002, 18, (10), pp. 13191331.
    42. 42)
      • 52. Li, H., Xie, L., Wang, Y.: ‘On robust control invariance of Boolean control networks’, Automatica, 2016, 68, pp. 392396.
    43. 43)
      • 13. Li, H., Wang, Y., Liu, Z.: ‘Stability analysis for switched Boolean networks under arbitrary switching signals’, IEEE Trans. Autom. Control, 2014, 59, (7), pp. 19781982.
    44. 44)
      • 109. Faryabi, B., Vahedi, G., Chamberland, J., et al: ‘Intervention in context-sensitive probabilistic Boolean networks revisited’, EURASIP J. Bioinform. Syst. Biol., 2009, 2009, (1), p. 1.
    45. 45)
      • 113. Gopalakrishnan, R., Marden, J.R., Wierman, A.: ‘An architectural view of game theoretic control’, ACM SIGMETRICS Perform. Eval. Rev., 2011, 38, pp. 3136.
    46. 46)
      • 23. Cheng, D., Qi, H., Li, Z., et al: ‘Stability and stabilization of Boolean networks’, Int. J. Robust Nonlinear Control, 2011, 21, (2), pp. 134156.
    47. 47)
      • 31. Laschov, D., Margaliot, M.: ‘Controllability of Boolean control networks via the perron–frobenius theory’, Automatica, 2012, 48, (6), pp. 12181223.
    48. 48)
      • 16. Li, F., Sun, J.: ‘Controllability of Boolean control networks with time delays in states’, Automatica, 2011, 47, (3), pp. 603607.
    49. 49)
      • 100. Chen, H., Liang, J., Lu, J.: ‘Partial synchronization of interconnected Boolean networks’, IEEE Trans. Syst. Man Cybern. Syst., 2016, 47, (1), pp. 258266, doi: 10.1109/TSMC.2015.2507162.
    50. 50)
      • 30. Li, H., Wang, Y.: ‘On reachability and controllability of switched Boolean control networks’, Automatica, 2012, 48, (11), pp. 29172922.
    51. 51)
      • 80. Xu, X., Hong, Y.: ‘Matrix approach to model matching of asynchronous sequential machines’, IEEE Trans. Autom. Control, 2013, 11, (58), pp. 29742979.
    52. 52)
      • 98. Li, F., Lu, X.: ‘Stability of a switched Boolean network via designing switching laws’, Qual. Theory Dyn. Syst., 2015, 15, pp. 112.
    53. 53)
      • 34. Liu, Y., Chen, H., Lu, J., et al: ‘Controllability of probabilistic Boolean control networks based on transition probability matrices’, Bul. Inst. Politeh. ‘Gheorghe Gheorghiu-Dej’ Bucur. Ser. Autom., 2015, 52, pp. 340345.
    54. 54)
      • 45. Li, R., Yang, M., Chu, T.: ‘Synchronization design of Boolean networks via the semi-tensor product method’, IEEE Trans. Neural Netw. Learn. Syst., 2013, 24, (6), pp. 9961001.
    55. 55)
      • 21. Li, H., Wang, Y.: ‘Output feedback stabilization control design for Boolean control networks’, Automatica, 2013, 49, (12), pp. 36413645.
    56. 56)
      • 35. Zhao, Y., Qi, H., Cheng, D.: ‘Input-state incidence matrix of Boolean control networks and its applications’, Syst. Control Lett., 2010, 59, (12), pp. 767774.
    57. 57)
      • 26. Liu, Y., Cao, J., Sun, L., et al: ‘Sampled-data state feedback stabilization of Boolean control networks’, Neural Comput., 2016, 28, (4), pp. 778799.
    58. 58)
      • 101. Laschov, D., Margaliot, M., Even, G.: ‘Observability of Boolean networks: a graph-theoretic approach’, Automatica, 2013, 49, (8), pp. 23512362.
    59. 59)
      • 66. Zhao, Y., Li, Z., Cheng, D.: ‘Optimal control of logical control networks’, IEEE Trans. Autom. Control, 2011, 56, (8), pp. 17661776.
    60. 60)
      • 32. Li, F., Sun, J.: ‘Controllability of probabilistic Boolean control networks’, Automatica, 2011, 47, (12), pp. 27652771.
    61. 61)
      • 114. Cheng, D.: ‘On finite potential games’, Automatica, 2014, 50, (7), pp. 17931801.
    62. 62)
      • 93. Zhang, K., Zhang, L., Mou, S.: ‘An application of invertibility of Boolean control networks to the control of the mammalian cell cycle’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2016, 14, (1), pp. 225229.
    63. 63)
      • 92. Li, F., Sun, J., Wu, Q.: ‘Observability of Boolean control networks with state time delays’, IEEE Trans. Neural Netw., 2011, 22, (6), pp. 948954.
    64. 64)
      • 19. Zhang, K., Zhang, L., Xie, L.: ‘Invertibility and nonsingularity of Boolean control networks’, Automatica, 2015, 60, pp. 155164.
    65. 65)
      • 9. Cheng, D., Qi, H.: ‘A linear representation of dynamics of Boolean networks’, IEEE Trans. Autom. Control, 2010, 55, (10), pp. 22512258.
    66. 66)
      • 91. Lu, J., Zhong, J., Li, L., et al: ‘Synchronization analysis of master-slave probabilistic Boolean networks’, Sci. Rep., 2015, 5, pp. 13437.
    67. 67)
      • 29. Cheng, D., Qi, H.: ‘Controllability and observability of Boolean control networks’, Automatica, 2009, 45, (7), pp. 16591667.
    68. 68)
      • 22. Li, F.: ‘Pinning control design for the stabilization of Boolean networks’, IEEE Trans. Neural Netw. Learn. Syst., 2015, 27, pp. 15851590.
    69. 69)
      • 94. Zhang, K., Zhang, L.: ‘Observability of Boolean control networks: a unified approach based on finite automata’, IEEE Trans. Autom. Control, 2016, 61, (9), pp. 27332738.
    70. 70)
      • 102. Laschov, D., Margaliot, M.: ‘On Boolean control networks with maximal topological entropy’, Automatica, 2014, 50, (11), pp. 29242928.
    71. 71)
      • 67. Zhao, G., Wang, Y., Li, H.: ‘Invertibility of higher order k-valued logical control networks and its application in trajectory control’, J. Franklin Inst., 2016, 353, (17), pp. 46674679.
    72. 72)
      • 55. Liu, Y., Chen, H., Wu, B., et al: ‘A mayer-type optimal control for multivalued logic control networks with undesirable states’, Appl. Math. Model., 2015, 39, (12), pp. 33573365.
    73. 73)
      • 15. Li, H., Wang, Y.: ‘Controllability analysis and control design for switched Boolean networks with state and input constraints’, SIAM J. Control Optim., 2015, 53, (5), pp. 29552979.
    74. 74)
      • 65. Cheng, D., Qi, H., Zhao, Y.: ‘Analysis and control of general logical networks–an algebraic approach’, Annu. Rev. Control, 2012, 36, (1), pp. 1125.
    75. 75)
      • 5. Xu, X., Hong, Y.: ‘Matrix expression and reachability analysis of finite automata’, J. Control Theory Appl., 2012, 10, (2), pp. 210215.
    76. 76)
      • 108. Li, F.: ‘Global stability at a limit cycle of switched Boolean networks under arbitrary switching signals’, Neurocomputing, 2014, 133, pp. 6366.
    77. 77)
      • 2. Cheng, D., He, F., Qi, H., et al: ‘Modeling, analysis and control of networked evolutionary games’, IEEE Trans. Autom. Control, 2015, 60, (9), pp. 24022415.
    78. 78)
      • 96. Li, H., Wang, Y., Guo, P.: ‘State feedback based output tracking control of probabilistic Boolean networks’, Inf. Sci., 2016, 349, pp. 111.
    79. 79)
      • 84. Liu, X., Zhu, J.: ‘On potential equations of finite games’, Automatica, 2016, 68, pp. 245253.
    80. 80)
      • 73. Wang, Y., Feng, J., Meng, M.: ‘Topological structure and optimal control of singular mix-valued logical networks’, Control Theory Technol., 2015, 13, (4), pp. 321332.
    81. 81)
      • 87. Chen, H., Li, X., Sun, J.: ‘Stabilization, controllability and optimal control of Boolean networks with impulsive effects and state constraints’, IEEE Trans. Autom. Control, 2015, 60, (3), pp. 806811.
    82. 82)
      • 57. Laschov, D., Margaliot, M.: ‘Minimum-time control of Boolean networks’, SIAM J. Control Optim., 2013, 51, (4), pp. 28692892.
    83. 83)
      • 110. Meng, M., Feng, J.: ‘Function perturbations in Boolean networks with its application in a d. melanogaster gene network’, Eur. J. Control, 2014, 20, (2), pp. 8794.
    84. 84)
      • 95. Zhang, L., Zhang, K.: ‘Controllability and observability of Boolean control networks with time-variant delays in states’, IEEE Trans. Neural Netw. Learn. Syst., 2013, 24, (9), pp. 14781484.
    85. 85)
      • 24. Chen, H., Sun, L., Liu, Y.: ‘Partial stability and stabilisation of Boolean networks’, Int. J. Syst. Sci., 2016, 47, (9), pp. 21192127.
    86. 86)
      • 78. Zhong, J., Lin, D.: ‘Driven stability of nonlinear feedback shift registers with inputs’, IEEE Trans. Commun., 2016, 64, (6), pp. 22742284.
    87. 87)
      • 79. Han, X., Chen, Z., Liu, Z., et al: ‘Calculation of siphons and minimal siphons in petri nets based on semi-tensor product of matrices’, IEEE Trans. Syst. Man Cybern. Syst., 2015, 47, (3), pp. 531536, doi: 10.1109/TSMC.2015.2507162.
    88. 88)
      • 43. Lu, J., Zhong, J., Tang, Y., et al: ‘Synchronization in output-coupled temporal Boolean networks’, Sci. Rep., 2014, 4, p. 6292.
    89. 89)
      • 112. Guo, P., Wang, Y., Li, H.: ‘Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method’, Automatica, 2013, 49, (11), pp. 33843389.
    90. 90)
      • 54. Li, F., Sun, J.: ‘Controllability and optimal control of a temporal Boolean network’, IEEE Trans. Neural Netw., 2012, 34, pp. 1017.
    91. 91)
      • 61. Zhao, Y., Kim, J., Filippone, M.: ‘Aggregation algorithm towards large-scale Boolean network analysis’, IEEE Trans. Autom. Control, 2013, 58, (8), pp. 19761985.
    92. 92)
      • 77. Zhao, D., Peng, H., Lixiang, L., et al: ‘Novel way to research nonlinear feedback shift register’, Sci. China Inform. Sci., 2014, 57, (9), pp. 114.
    93. 93)
      • 51. Zou, Y., Zhu, J.: ‘Kalman decomposition for Boolean control networks’, Automatica, 2015, 54, pp. 6571.
    94. 94)
      • 17. Hinkelmann, F., Brandon, M., Guang, B., et al: ‘Adam: analysis of discrete models of biological systems using computer algebra’, BMC Bioinform., 2011, 12, (1), p. 295.
    95. 95)
      • 44. Zhang, H., Tian, H., Wang, Z., et al: ‘Synchronization analysis and design of coupled Boolean networks based on periodic switching sequences’, IEEE Trans. Neural Netw. Learn. Syst., 2016, 27, (11), pp. 27542759.
    96. 96)
      • 10. Zhong, J., Lu, J., Liu, Y., et al: ‘Synchronization in an array of output-coupled Boolean networks with time delay’, IEEE Trans. Neural Netw. Learn. Syst., 2014, 25, (12), pp. 22882294.
    97. 97)
      • 40. Yang, M., Li, T., Chu, R.: ‘Controller design for disturbance decoupling of Boolean control networks’, Automatica, 2013, 49, (1), pp. 273277.
    98. 98)
      • 37. Cheng, D.: ‘Disturbance decoupling of Boolean control networks’, IEEE Trans. Autom. Control, 2011, 56, (1), pp. 210.
    99. 99)
      • 83. Zhu, B., Xia, X., Wu, Z.: ‘Evolutionary game theoretic demand-side management and control for a class of networked smart grid’, Automatica, 2016, 70, pp. 94100.
    100. 100)
      • 41. Li, R., Chu, T.: ‘Complete synchronization of Boolean networks.’, IEEE Trans. Neural Netw. Learn. Syst., 2012, 23, (5), p. 840.
    101. 101)
      • 59. Cheng, D., Qi, H., Zhao, Y.: ‘An introduction to semi-tensor product of matrices and its applications’ (World Scientific, 2012).
    102. 102)
      • 33. Lu, J., Zhong, J., Huang, C., et al: ‘On pinning controllability of Boolean control networks’, IEEE Trans. Autom. Control, 2016, 61, (6), pp. 16581663.
    103. 103)
      • 6. Liu, Z., Wang, Y., Cheng, D.: ‘Nonsingularity of feedback shift registers’, Automatica, 2015, 55, pp. 247253.
    104. 104)
      • 7. Shmulevich, I., Dougherty, E.R., Kim, S., et al: ‘Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2002, 18, (2), pp. 261274.
    105. 105)
      • 42. Liu, Y., Sun, L., Lu, J., et al: ‘Feedback controller design for the synchronization of Boolean control networks’, IEEE Trans. Neural Netw. Learn. Syst., 2016, 27, (9), pp. 19911996.
    106. 106)
      • 46. Li, H., Wang, Y., Xie, L.: ‘Output tracking control of Boolean control networks via state feedback: constant reference signal case’, Bul. Inst. Politeh. ‘Gheorghe Gheorghiu-Dej’ Bucur. Ser. Autom., 2015, 59, pp. 5459.
    107. 107)
      • 75. Wu, Y., Shen, T.: ‘An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems’, Syst. Control Lett., 2015, 82, pp. 108114.
    108. 108)
      • 56. Fornasini, E., Valcher, M.E.: ‘Optimal control of Boolean control networks’, IEEE Trans. Autom. Control, 2014, 59, (5), pp. 12581270.
    109. 109)
      • 68. Liu, Z., Wang, Y.: ‘Reachability/controllability of high order mix-valued logical networks’, J. Syst. Sci. Complex., 2013, 26, (3), pp. 341349.
    110. 110)
      • 18. Hochma, G., Margaliot, M., Fornasini, E., et al: ‘Symbolic dynamics of Boolean control networks’, Automatica, 2013, 49, (8), pp. 25252530.
    111. 111)
      • 36. Liu, Y., Chen, H., Wu, B.: ‘Controllability of Boolean control networks with impulsive effects and forbidden states’, Math. Methods Appl. Sci., 2014, 37, (1), pp. 19.
    112. 112)
      • 85. Li, H., Wang, Y.: ‘A matrix approach to latticized linear programming with fuzzy-relation inequality constraints’, IEEE Trans. Fuzzy Syst., 2013, 21, (4), pp. 781788.
    113. 113)
      • 28. Li, R., Yang, M., Chu, T.: ‘State feedback stabilization for Boolean control networks’, IEEE Trans. Autom. Control, 2013, 58, (7), pp. 18531857.
    114. 114)
      • 27. Li, H., Wang, Y., Liu, Z.: ‘Simultaneous stabilization for a set of Boolean control networks’, Syst. Control Lett., 2013, 62, (12), pp. 11681174.
    115. 115)
      • 49. Cheng, D., Li, Z., Qi, H.: ‘Realization of Boolean control networks’, Bul. Inst. Politeh. ‘Gheorghe Gheorghiu-Dej’ Bucur. Ser. Autom., 2010, 46, (1), pp. 6269.
    116. 116)
      • 105. Li, F.: ‘Feedback control design for the complete synchronisation of two coupled Boolean networks’, Int. J. Syst. Sci., 2016, 47, (12), pp. 29963003.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2016.1659
Loading

Related content

content/journals/10.1049/iet-cta.2016.1659
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address