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A survey on applications of semi-tensor product method in engineering

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  • Special Focus on Analysis and Control of Finite-Valued Network Systems
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Abstract

Semi-tensor product (STP) of matrices has attracted more and more attention from both control theory and engineering in the last two decades. This paper presents a comprehensive survey on the applications of STP method in engineering. Firstly, some preliminary results on STP method are recalled. Secondly, some applications of STP method in engineering, including gene regulation, power system, wireless communication, smart grid, information security, combustion engine and vehicle control, are reviewed. Finally, some potential applications of STP method are predicted.

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References

  1. Cheng D Z. Semi-tensor product of matrices and its application to Morgan’s problem. Sci China Ser F-Inf Sci, 2001, 44: 195–212

    MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  3. Cheng D Z, Qi H S. Semi-tensor Product of Matrices-Theory and Applications. Beijing: Science Press, 2007

    Google Scholar 

  4. Cheng D Z, Qi H S, Li Z Q. Analysis and Control of Boolean Networks: a Semi-tensor Product Approach. London: Springer-Verlag, 2011

    Book  MATH  Google Scholar 

  5. Cheng D Z, Ma J, Lu Q, et al. Quadratic form of stable sub-manifold for power systems. Int J Robust Nonlinear Control, 2004, 14: 773–788

    Article  MathSciNet  MATH  Google Scholar 

  6. Cheng D Z, Hu X M, Wang Y Z. Non-regular feedback linearization of nonlinear systems via a normal form algorithm. Automatica, 2004, 40: 439–447

    Article  MathSciNet  MATH  Google Scholar 

  7. Cheng D Z, Yang G W, Xi Z R. Nonlinear systems possessing linear symmetry. Int J Robust Nonlinear Control, 2010, 17: 51–81

    Article  MathSciNet  MATH  Google Scholar 

  8. Li Z Q, Qiao Y P, Qi H S, et al. Stability of switched polynomial systems. J Syst Sci Complex, 2008, 21: 362–377

    Article  MathSciNet  MATH  Google Scholar 

  9. Fornasini E, Valcher M. Recent developments in Boolean networks control. J Control Decis, 2016, 3: 1–18

    Article  MathSciNet  Google Scholar 

  10. Cheng D Z, Qi H S. State-space analysis of Boolean networks. IEEE Trans Neural Netw, 2010, 21: 584–594

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. Cheng D Z, Qi H S, Li Z Q, et al. Stability and stabilization of Boolean networks. Int J Robust Nonlinear Control, 2011, 21: 134–156

    Article  MathSciNet  MATH  Google Scholar 

  13. Li F F, Sun J T. Asymptotic stability of a genetic network under impulsive control. Phys Lett A, 2010, 374: 3177–3184

    Article  MATH  Google Scholar 

  14. Li F F. Global stability at a limit cycle of switched Boolean networks under arbitrary switching signals. Neurocomputing, 2014, 133: 63–66

    Article  Google Scholar 

  15. Chen H, Sun J T. Global stability and stabilization of switched Boolean network with impulsive effects. Appl Math Comput, 2013, 224: 625–634

    MathSciNet  MATH  Google Scholar 

  16. Fornasini E, Valcher M E. On the periodic trajectories of Boolean control networks. Automatica, 2013, 49: 1506–1509

    Article  MathSciNet  MATH  Google Scholar 

  17. Li H T, Wang Y Z. Consistent stabilizability of switched Boolean networks. Neural Netw, 2013, 46: 183–189

    Article  MATH  Google Scholar 

  18. Guo Y Q, Wang P, Gui W H, et al. Set stability and set stabilization of Boolean control networks based on invariant subsets. Automatica, 2015, 61: 106–112

    Article  MathSciNet  MATH  Google Scholar 

  19. Li H T, Wang Y Z, Liu Z B. Stability analysis for switched Boolean networks under arbitrary switching signals. IEEE Trans Autom Control, 2014, 59: 1978–1982

    Article  MathSciNet  MATH  Google Scholar 

  20. Li H T, Wang Y Z. Robust stability and stabilisation of Boolean networks with disturbance inputs. Int J Syst Sci, 2016, 48: 750–756

    Article  MathSciNet  MATH  Google Scholar 

  21. Li H T, Wang Y Z. Lyapunov-based stability and construction of Lyapunov functions for Boolean networks. SIAM J Control Optim, 2017, 55: 3437–3457

    Article  MathSciNet  MATH  Google Scholar 

  22. Meng M, Liu L, Feng G. Stability and l1 gain analysis of Boolean networks with Markovian jump parameters. IEEE Trans Autom Control, 2017, 62: 4222–4228

    Article  MATH  Google Scholar 

  23. Jia G Y, Meng M, Feng J E. Function perturbation of mix-valued logical networks with impacts on limit sets. Neurocomputing, 2016, 207: 428–436

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhao Y, Cheng D Z, Qi H S. Input-state incidence matrix of Boolean control networks and its applications. Syst Control Lett, 2010, 59: 767–774

    Article  MathSciNet  MATH  Google Scholar 

  26. Laschov D, Margaliot M. Controllability of Boolean control networks via the Perron-Frobenius theory. Automatica, 2012, 48: 1218–1223

    Article  MathSciNet  MATH  Google Scholar 

  27. Chen H, Sun J T. A new approach for global controllability of higher order Boolean control network. Neural Netw, 2013, 39: 12–17

    Article  MATH  Google Scholar 

  28. Chen H W, Sun L J, Liu Y. Partial stability and stabilisation of Boolean networks. Int J Syst Sci, 2016, 47: 2119–2127

    Article  MathSciNet  MATH  Google Scholar 

  29. Li F F, Tang Y. Set stability for switched Boolean control networks. Automatica, 2017, 78: 223–230

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  34. Han M, Liu Y, Tu Y S. Controllability of Boolean control networks with time delays both in states and inputs. Neurocomputing, 2014, 129: 467–475

    Article  Google Scholar 

  35. Li H T, Wang Y Z. Controllability analysis and control design for switched Boolean networks with state and input constraints. SIAM J Control Optim, 2015, 53: 2955–2979

    Article  MathSciNet  MATH  Google Scholar 

  36. Liu Y, Chen H W, Wu B. Controllability of Boolean control networks with impulsive effects and forbidden states. Math Method Appl Sci, 2014, 37: 1–9

    Article  MATH  Google Scholar 

  37. Liu Y, Chen H W, Lu J Q, et al. Controllability of probabilistic Boolean control networks based on transition probability matrices. Automatica, 2015, 52: 340–345

    Article  MathSciNet  MATH  Google Scholar 

  38. Luo C, Wang X Y, Liu H. Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update. Sci Rep, 2014, 4: 07522

    Article  Google Scholar 

  39. Zhang L J, Zhang K Z. Controllability of time-variant Boolean control networks and its application to Boolean control networks with finite memories. Sci China Inf Sci, 2013, 56: 108201

    MathSciNet  Google Scholar 

  40. Chen H W, Liang J L, Wang Z D. Pinning controllability of autonomous Boolean control networks. Sci China Inf Sci, 2016, 59: 070107

    Article  Google Scholar 

  41. Li H T, Wang Y Z. On reachability and controllability of switched Boolean control networks. Automatica, 2012, 48: 2917–2922

    Article  MathSciNet  MATH  Google Scholar 

  42. Liu Y, Lu J Q, Wu B. Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks. ESAIM Control Optim Calc Var, 2014, 20: 158–173

    Article  MathSciNet  MATH  Google Scholar 

  43. Lu J Q, Zhong J, Huang C, et al. On pinning controllability of Boolean control networks. IEEE Trans Autom Control, 2016, 61: 1658–1663

    Article  MathSciNet  MATH  Google Scholar 

  44. Lu J Q, Zhong J, Ho D W C, et al. On controllability of delayed Boolean control networks. SIAM J Control Optim, 2016, 54: 475–494

    Article  MathSciNet  MATH  Google Scholar 

  45. 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

    Article  Google Scholar 

  46. Cheng D Z, Qi H S, Liu T, et al. A note on observability of Boolean control networks. Syst Control Lett, 2016, 87: 76–82

    Article  MathSciNet  MATH  Google Scholar 

  47. Fornasini E, Valcher M E. Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans Autom Control, 2013, 58: 1390–1401

    Article  MathSciNet  MATH  Google Scholar 

  48. Laschov D, Margaliot M, Even G. Observability of Boolean networks: a graph-theoretic approach. Automatica, 2013, 49: 2351–2362

    Article  MathSciNet  MATH  Google Scholar 

  49. Li F F, Sun J T, Wu Q D. Observability of Boolean control networks with state time delays. IEEE Trans Neural Netw, 2011, 22: 948–954

    Article  Google Scholar 

  50. Li R, Yang M, Chu T G. Observability conditions of Boolean control networks. Int J Robust Nonlinear Control, 2014, 24: 2711–2723

    Article  MathSciNet  MATH  Google Scholar 

  51. Zhang K Z, Zhang L J. Observability of Boolean control networks: a unified approach based on finite automata. IEEE Trans Autom Control, 2016, 61: 2733–2738

    Article  MathSciNet  MATH  Google Scholar 

  52. Zhang K Z, Zhang L J, Xie L H. Finite automata approach to observability of switched Boolean control networks. Nonlinear Anal Hybrid Syst, 2016, 19: 186–197

    Article  MathSciNet  MATH  Google Scholar 

  53. Zhu Q X, Liu Y, Lu J Q, et al. Observability of Boolean control networks. Sci China Inf Sci, 2018, 61: 092201

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  56. Li R, Yang M, Chu T G. State feedback stabilization for probabilistic Boolean networks. Automatica, 2014, 50: 1272–1278

    Article  MathSciNet  MATH  Google Scholar 

  57. Bof N, Fornasini E, Valcher M E. Output feedback stabilization of Boolean control networks. Automatica, 2015, 57: 21–28

    Article  MathSciNet  MATH  Google Scholar 

  58. Chen H, Li X D, Sun J T. Stabilization, controllability and optimal control of Boolean networks with impulsive effects and state constraints. IEEE Trans Autom Control, 2015, 60: 806–811

    Article  MathSciNet  MATH  Google Scholar 

  59. Li F F, Sun J T. Stability and stabilization of Boolean networks with impulsive effects. Syst Control Lett, 2012, 61: 1–5

    Article  MathSciNet  MATH  Google Scholar 

  60. Li F F. Pinning control design for the stabilization of Boolean networks. IEEE Trans Neural Netw Learn Syst, 2015, 27: 1585–1590

    Article  MathSciNet  Google Scholar 

  61. Li H T, Wang Y Z. Output feedback stabilization control design for Boolean control networks. Automatica, 2013, 49: 3641–3645

    Article  MathSciNet  MATH  Google Scholar 

  62. Liu Y, Cao J D, Sun L J, et al. Sampled-data state feedback stabilization of Boolean control networks. Neural Comput, 2016, 28: 778–799

    Article  Google Scholar 

  63. Li H T, Wang Y Z, Liu Z B. Simultaneous stabilization for a set of Boolean control networks. Syst Control Lett, 2013, 62: 1168–1174

    Article  MathSciNet  MATH  Google Scholar 

  64. Li H T, Wang Y Z. Minimum-time state feedback stabilization of constrained Boolean control networks. Asian J Control, 2016, 18: 1688–1697

    Article  MathSciNet  MATH  Google Scholar 

  65. Li H T, Wang Y Z. Further results on feedback stabilization control design of Boolean control networks. Automatica, 2017, 83: 303–308

    Article  MathSciNet  MATH  Google Scholar 

  66. Li H T, Ding X Y, Alsaedi A, et al. Stochastic set stabilization of n-person random evolutionary Boolean games and its applications. IET Control Theory Appl, 2017, 11: 2152–2160

    Article  Google Scholar 

  67. Zhong J, Ho D W C, Lu J Q, et al. Global robust stability and stabilization of Boolean network with disturbances. Automatica, 2017, 84: 142–148

    Article  MathSciNet  MATH  Google Scholar 

  68. Liu R J, Lu J Q, Liu Y, et al. Delayed feedback control for stabilization of Boolean control networks with state delay. IEEE Trans Neural Netw Learn Systems, 2017. doi: 10.1109/TNNLS.2017.2659386

    Google Scholar 

  69. Ding X Y, Li H T, Yang Q Q, et al. Stochastic stability and stabilization of n-person random evolutionary Boolean games. Appl Math Comput, 2017, 306: 1–12

    MathSciNet  Google Scholar 

  70. 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

    Article  Google Scholar 

  71. Li F F, Lu X W. Complete synchronization of temporal Boolean networks. Neural Netw, 2013, 44: 72–77

    Article  MATH  Google Scholar 

  72. Li F F, Yu Z X. Anti-synchronization of two coupled Boolean networks. J Franklin Inst, 2016, 353: 5013–5024

    Article  MathSciNet  MATH  Google Scholar 

  73. Li R, Chu T G. Complete synchronization of Boolean networks. IEEE Trans Neural Netw Learn Syst, 2012, 23: 840–846

    Article  Google Scholar 

  74. Lu J Q, Zhong J, Li L L, et al. Synchronization analysis of master-slave probabilistic Boolean networks. Sci Rep, 2015, 5: 13437

    Article  Google Scholar 

  75. Chen H W, Liang J L, Liu Y, et al. Synchronisation analysis of Boolean networks based on equivalence. IET Control Theory Appl, 2015, 9: 2242–2248

    Article  MathSciNet  Google Scholar 

  76. Liu Y, Sun L J, Lu J Q, et al. Feedback controller design for the synchronization of Boolean control networks. IEEE Trans Neural Netw Learn Syst, 2016, 27: 1991–1996

    Article  MathSciNet  Google Scholar 

  77. Li F F. Pinning control design for the synchronization of two coupled Boolean networks. IEEE Trans Circ Syst II Express Brief, 2016, 63: 309–313

    Google Scholar 

  78. Zhong J, Lu J Q, Huang T W, et al. Controllability and synchronization analysis of identical-hierarchy mixed-valued logical control networks. IEEE Trans Cybernet, 2017, 47: 3482–3493

    Article  Google Scholar 

  79. Zhong J, Lu J Q, Huang T W, et al. Synchronization of master-slave Boolean networks with impulsive effects: necessary and sufficient criteria. Neurocomputing, 2014, 143: 269–274

    Article  Google Scholar 

  80. Chen H W, Liang J L, Lu J Q. Partial synchronization of interconnected Boolean networks. IEEE Trans Cybern, 2017, 47: 258–266

    Article  Google Scholar 

  81. Tian H, Wang Z S, Hou Y F, et al. State feedback controller design for synchronization of master-slave Boolean networks based on core input-state cycles. Neurocomputing, 2016, 174: 1031–1037

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  83. Meng M, Feng J E. Topological structure and the disturbance decoupling problem of singular Boolean networks. IET Control Theory Appl, 2014, 8: 1247–1255

    Article  MathSciNet  Google Scholar 

  84. Cheng D Z. Disturbance decoupling of Boolean control networks. IEEE Trans Autom Control, 2011, 56: 2–10

    Article  MathSciNet  MATH  Google Scholar 

  85. Li H T, Wang Y Z, Xie L H, et al. Disturbance decoupling control design for switched Boolean control networks. Syst Control Lett, 2014, 72: 1–6

    Article  MathSciNet  MATH  Google Scholar 

  86. Zhang L Q, Feng J E, Feng X H, et al. Further results on disturbance decoupling of mix-valued logical networks. IEEE Trans Autom Control, 2014, 59: 1630–1634

    Article  Google Scholar 

  87. Liu Y, Li B W, Lou J G. Disturbance decoupling of singular Boolean control networks. IEEE/ACM Trans Comput Biol Bioinf, 2016, 13: 1194–1200

    Article  Google Scholar 

  88. Liu Z B, Wang Y Z. Disturbance decoupling of mix-valued logical networks via the semi-tensor product method. Automatica, 2012, 48: 1839–1844

    Article  MathSciNet  MATH  Google Scholar 

  89. Liu Y, Li B W, Lu J Q, et al. Pinning control for the disturbance decoupling problem of Boolean networks. IEEE Trans Autom Control, 2017. doi: 10.1109/TAC.2017.2715181

    Google Scholar 

  90. Laschov D, Margaliot M. A maximum principle for single-input Boolean control networks. IEEE Trans Autom Control, 2011, 56: 913–917

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  93. Fornasini E, Valcher M E. Optimal control of Boolean control networks. IEEE Trans Autom Control, 2014, 59: 1258–1270

    Article  MathSciNet  MATH  Google Scholar 

  94. 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

    MathSciNet  MATH  Google Scholar 

  95. Liu Y, Chen H W, Wu B, et al. A Mayer-type optimal control for multivalued logic control networks with undesirable states. Appl Math Model, 2015, 39: 3357–3365

    Article  MathSciNet  Google Scholar 

  96. Wu Y H, Shen T L. An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems. Syst Control Lett, 2015, 82: 108–114

    Article  MATH  Google Scholar 

  97. Cheng D Z, Zhao Y, Xu T T. Receding horizon based feedback optimization for mix-valued logical networks. IEEE Trans Autom Control, 2015, 60: 3362–3366

    Article  MathSciNet  MATH  Google Scholar 

  98. Li F F, Lu X W, Yu Z X. Optimal control algorithms for switched Boolean network. J Franklin Inst, 2014, 351: 3490–3501

    Article  MathSciNet  MATH  Google Scholar 

  99. Li H T, Wang Y Z, Guo P L. State feedback based output tracking control of probabilistic Boolean networks. Inf Sci, 2016, 349: 1–11

    MathSciNet  Google Scholar 

  100. 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

    Article  MathSciNet  MATH  Google Scholar 

  101. Li H T, Xie L H, Wang Y Z. Output regulation of Boolean control networks. IEEE Trans Autom Control, 2017, 62: 2993–2998

    Article  MathSciNet  MATH  Google Scholar 

  102. Li H T, Wang Y Z. Output tracking of switched Boolean networks under open-loop/closed-loop switching signals. Nonlinear Anal Hybrid Syst, 2016, 22: 137–146

    Article  MathSciNet  MATH  Google Scholar 

  103. Li H T, Song P P, Yang Q Q. Pinning control design for robust output tracking of k-valued logical networks. J Franklin Inst, 2017, 354: 3039–3053

    Article  MathSciNet  MATH  Google Scholar 

  104. Liu Y S, Zheng Y T, Li H T, et al. Control design for output tracking of delayed Boolean control networks. J Comput Appl Math, 2018, 327: 188–195

    Article  MathSciNet  MATH  Google Scholar 

  105. Li H T, Wang Y Z, Guo P L. Output reachability analysis and output regulation control design of Boolean control networks. Sci China Inf Sci, 2017, 60: 022202

    Article  Google Scholar 

  106. Fornasini E, Valcher M. Fault detection analysis of Boolean control networks. IEEE Trans Autom Control, 2015, 60: 2734–2739

    Article  MathSciNet  MATH  Google Scholar 

  107. Zhao G D, Wang Y Z, Li H T. Invertibility of higher order k-valued logical control networks and its application in trajectory control. J Franklin Inst, 2016, 353: 4667–4679

    Article  MathSciNet  MATH  Google Scholar 

  108. Li H T, Xie L H, Wang Y Z. On robust control invariance of Boolean control networks. Automatica, 2016, 68: 392–396

    Article  MathSciNet  MATH  Google Scholar 

  109. Cheng D Z, Li Z Q, Qi H S. Realization of Boolean control networks. Automatica, 2010, 46: 62–69

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  111. Zou Y L, Zhu J D. Kalman decomposition for Boolean control networks. Automatica, 2015, 54: 65–71

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  113. Meng M, Lam J, Feng J E, et al. l1-gain analysis and model reduction problem for Boolean control networks. Inf Sci, 2016, 348: 68–83

    Article  Google Scholar 

  114. Liu Y, Cao J D, Li B W, et al. Normalization and solvability of dynamic-algebraic Boolean networks. IEEE Trans Neural Netw Learn Syst, 2017. doi:10.1109/TNNLS.2017.2715060

    Google Scholar 

  115. Xie D, Peng H P, Li L X, et al. Semi-tensor compressed sensing. Digit Signal Process, 2016, 58: 85–92

    Article  Google Scholar 

  116. Jiang P, Yu H L, Wang S G. Optimization of expert system via semi-tensor product. In: Proceedings of the 32nd Youth Academic Annual Conference of Chinese Association of Automation, Hefei, 2017

    Book  Google Scholar 

  117. Li H T, Ding X Y, Yang Q Q, et al. Algebraic formulation and Nash equilibrium of competitive diffusion games. Dynam Games Appl, 2017. doi: 10.1007/s13235-017-0228-4

    Google Scholar 

  118. Cheng D Z, Qi H S, Xue A. A survey on semi-tensor product of matrices. J Syst Sci Complex, 2007, 20: 304–322

    Article  MathSciNet  MATH  Google Scholar 

  119. Cheng D Z, Qi H S, Zhao Y. Analysis and control of general logical networks-An algebraic approach. Annu Rev Control, 2012, 36: 11–25

    Article  Google Scholar 

  120. Cheng D Z, Qi H S, He F, et al. Semi-tensor product approach to networked evolutionary games. Control Theory Technol, 2014, 12: 198–214

    Article  MathSciNet  MATH  Google Scholar 

  121. Lu J Q, Li H T, Liu Y, et al. Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems. IET Control Theory Appl, 2017, 11: 2040–2047

    Article  Google Scholar 

  122. Cheng D Z, Qi H S. Principle and range of possible applications of semi-tensor product of matrices. J Syst Sci Math Sci, 2012, 32: 1488–1496

    MathSciNet  MATH  Google Scholar 

  123. Cheng D Z, Qi H S. Algebraic state space approach to logical dynamic systems and its applications. Control Theory Appl, 2014, 31: 1632–1639

    MATH  Google Scholar 

  124. Zhang K Z, Zhang L J, Mou S S. An application of invertibility of Boolean control networks to the control of the mammalian cell cycle. IEEE/ACM Trans Comput Biol Bioinform, 2017, 14: 225–229

    Article  Google Scholar 

  125. Meng M, Feng J E. Function perturbations in Boolean networks with its application in a D. melanogaster gene network. Eur J Control, 2014, 20: 87–94

    Article  MathSciNet  MATH  Google Scholar 

  126. Sun Y J, Liu F, Mei S W. Polynomial approximation of a nonlinear system and its application to power system (I): theoretical justification. Elect Mach Control, 2010, 14: 19–30

    Google Scholar 

  127. Sun Y J, Liu F, Mei S W. Polynomial approximation of a nonlinear system and its application to power system (II): applications. Elect Mach Control, 2010, 14: 7–12

    Google Scholar 

  128. Ma J, Cheng D Z, Mei S W, et al. Approximation of the boundary of power system stability region based on semi-tensor theory part one theoretical basis. Autom Elect Power Syst, 2006, 30: 1–5

    Google Scholar 

  129. Ma J, Cheng D, Mei S W, et al. Approximation of the boundary of power system stability region based on semi-tensor theory part two application. Automa Elect Power Syst, 2006, 30: 7–12

    Google Scholar 

  130. 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

    Article  MathSciNet  MATH  Google Scholar 

  131. Xu M R, Wang Y Z, Wei A R. Robust graph coloring based on the matrix semi-tensor product with application to examination timetabling. Control Theory Technol, 2014, 12: 187–197

    Article  MathSciNet  MATH  Google Scholar 

  132. Xu M R, Wang Y Z. Conflict-free coloring problem with appliction to frequency assignment. J Shandong Univ, 2015, 45: 64–69

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  134. Cheng D Z, He F H, Qi H S, et al. Modeling, analysis and control of networked evolutionary games. IEEE Trans Autom Control, 2015, 60: 2402–2415

    Article  MathSciNet  MATH  Google Scholar 

  135. 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

    Article  Google Scholar 

  136. Zhao G D, Wang Y Z, Li H T. A matrix approach to modeling and optimization for dynamic games with random entrance. Appl Math Comput, 2016, 290: 9–20

    MathSciNet  Google Scholar 

  137. Guo P L, Wang Y Z, Li H T. Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method. Automatica, 2013, 49: 3384–3389

    Article  MathSciNet  MATH  Google Scholar 

  138. Zhu B, Xia X H, Wu Z. Evolutionary game theoretic demand-side management and control for a class of networked smart grid. Automatica, 2016, 70: 94–100

    Article  MathSciNet  MATH  Google Scholar 

  139. Liu X Y, Zhu J D. On potential equations of finite games. Automatica, 2016, 68: 245–253

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  141. Xu X R, Hong Y G. Matrix expression and reachability analysis of finite automata. J Control Theory Appl, 2012, 10: 210–215

    Article  MathSciNet  Google Scholar 

  142. Han X G, Chen Z Q, Liu Z X, et al. Calculation of siphons and minimal siphons in petri nets based on semi-tensor product of matrices. IEEE Trans Syst Man Cybern Syst, 2017, 47: 531–536

    Article  Google Scholar 

  143. Yan Y Y, Chen Z Q, Liu Z X. Semi-tensor product of matrices approach to reachability of finite automata with application to language recognition. Front Comput Sci, 2014, 8: 948–957

    Article  MathSciNet  Google Scholar 

  144. Yan Y Y, Chen Z Q, Liu Z X. Semi-tensor product approach to controllability and stabilizability of finite automata. J Syst Eng Elect, 2015, 26: 134–141

    Article  Google Scholar 

  145. 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

    MathSciNet  Google Scholar 

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

    Google Scholar 

  147. Liu Z B, Wang Y Z, Cheng D Z. Nonsingularity of feedback shift registers. Automatica, 2015, 55: 247–253

    Article  MathSciNet  Google Scholar 

  148. Wu Y H, Kumar M, Shen T L. A stochastic logical system approach to model and optimal control of cyclic variation of residual gas fraction in combustion engines. Appl Therm Eng, 2016, 93: 251–259

    Article  Google Scholar 

  149. Wu Y H, Shen T L. Policy iteration approach to control residual gas fraction in IC engines under the framework of stochastic logical dynamics. IEEE Trans Control Syst Technol, 2017, 25: 1100–1107

    Article  Google Scholar 

  150. Kang M X, Wu Y H, Shen T L. Logical control approach to fuel efficiency optimization for commuting vehicles. Int J Autom Technol, 2017, 18: 535–546

    Article  Google Scholar 

  151. Cheng D Z, Feng J E, Lv H L. Solving fuzzy relational equations via semitensor product. IEEE Trans Fuzzy Syst, 2012, 20: 390–396

    Article  Google Scholar 

  152. Feng J E, Lv H L, Cheng D Z. Multiple fuzzy relation and its application to coupled fuzzy control. Asian J Control, 2013, 15: 1313–1324

    Article  MathSciNet  MATH  Google Scholar 

  153. Li H T, Wang Y Z. A matrix approach to latticized linear programming with fuzzy-relation inequality constraints. IEEE Trans Fuzzy Syst, 2013, 21: 781–788

    Article  Google Scholar 

  154. Duan P Y, Lv H L, Feng J E, et al. Fuzzy relation matrix control system for indoor thermal comfort. Control Theory Appl, 2013, 30: 215–221

    Google Scholar 

  155. Li H T, Wang Y Z. Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method. Automatica, 2012, 48: 688–693

    Article  MathSciNet  MATH  Google Scholar 

  156. Liu Z B, Wang Y Z, Li H T. New approach to derivative calculation of multi-valued logical functions with application to fault detection of digital circuits. IET Control Theory Appl, 2014, 8: 554–560

    Article  MathSciNet  Google Scholar 

  157. Jia Y L, Yang X B. Optimization of control parameters based on genetic algorithms for spacecraft attitude tracking with input constraints. Neurocomputing, 2016, 177: 334–341

    Article  Google Scholar 

  158. Guo P L, Wang Y Z. Matrix expression and vaccination control for epidemic dynamics over dynamic networks. Control Theory Technol, 2016, 14: 39–48

    Article  MathSciNet  MATH  Google Scholar 

  159. Jiang P, Wang Y Z, Ge A D. Multivariable fuzzy control based mobile robot odor source localization via semitensor product. Math Probl Eng, 2015, 2015: 736720

    MathSciNet  Google Scholar 

  160. Kauffman S A. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 1969, 22: 437–467

    Article  MathSciNet  Google Scholar 

  161. 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

    Article  MathSciNet  Google Scholar 

  162. Zhang K Z, Zhang L J, Xie L H. Invertibility and nonsingularity of Boolean control networks. Automatica, 2015, 60: 155–164

    Article  MathSciNet  MATH  Google Scholar 

  163. Li H T, Wang Y Z. Logical matrix factorization with application to topological structure analysis of Boolean network. IEEE Trans Autom Control, 2015, 60: 1380–1385

    Article  MathSciNet  MATH  Google Scholar 

  164. Xue A C, Wu F F, Lu Q, et al. Power system dynamic security region and its approximation. IEEE Trans Circ Syst I Regul Pap, 2006, 53: 2849–2859

    Article  MathSciNet  MATH  Google Scholar 

  165. Xue A C, Mei S W, Lu Q, et al. Approximation for the dynamic security region of network-reduction power systems. Autom Elect Power Syst, 2005, 29: 18–23

    Google Scholar 

  166. Xue A C, Hu W, Mei S W, et al. Comparison of linear approximations for the dynamic security region of networkreduction power system. In: Proceedings of 2006 IEEE Power Engineering Society General Meeting, Montreal, 2006

    Google Scholar 

  167. Ye J, Mei S W, Xue A C. Transient voltage stability analysis based on second-order approximation of stability boundary. Mod Elect Power, 2005, 22: 1–6

    Google Scholar 

  168. Wang Y H, Mei S W. Analysis of long- and medium-term power system voltage stability based on semi-tensor product and quasi-steady-state time domain simulation. Power Syst Technol, 2011, 35: 39–44

    Google Scholar 

  169. Ge A D, Wang Y Z, Wei A R, et al. Control design for multi-variable fuzzy systems with application to parallel hybrid electric vehicles. Control Theory Appl, 2013, 30: 998–1004

    Google Scholar 

  170. Eilenberg S. Automata, Languages, and Machines. New York: Academic Press, 1976

    MATH  Google Scholar 

  171. Cassandras C, Lafortune S. Introduction to Discrete Event Systems. New York: Springer-Verlag, 2008

    Book  MATH  Google Scholar 

  172. Lamego M. Automata control systems. IET Control Theory Appl, 2007, 1: 358–371

    Article  Google Scholar 

  173. Womham W, Ramadge P. On the supremal contrallable sublanguage of a given language. SIAM J Control Optim, 1987, 25: 637–659

    Article  MathSciNet  Google Scholar 

  174. Xu X R, Zhang Y Q, Hong Y G. Matrix approach to stabilizability of deterministic finite automata. In: Proceedings of American Control Conference (ACC), Washington, 2013. 3242–3247

    Google Scholar 

  175. Xu X R, Hong Y G. Observability analysis and observer design for finite automata via matrix approach. IET Control Theory Appl, 2013, 7: 1609–1615

    Article  MathSciNet  Google Scholar 

  176. Choy J, Chew G H, Khoo K, et al. Cryptographic properties and application of a generalized unbalanced Feistel network structure. Cryptogr Commun, 2011, 3: 141–164

    Article  MathSciNet  MATH  Google Scholar 

  177. Moon T K, Veeranmachneni S. Linear feedback shift registers as vector quantisation codebooks. Elect Lett, 1999, 35: 1919–1920

    Article  Google Scholar 

  178. Hellebrand S, Rajski J, Tarnick S, et al. Built-in test for circuits with scan based on reseeding of multiple-polynomial linear feedback shift registers. IEEE Trans Comput, 1995, 44: 223–233

    Article  MATH  Google Scholar 

  179. Raychaudlhuri A. Further results on T-coloring and frequency assignment problems. SIAM J Discrete Math, 1994, 7: 605–613

    Article  MathSciNet  Google Scholar 

  180. Box F. A heuristic technique for assigning frequencies to mobile radio nets. IEEE Trans Vehicle Technol, 1978, 27: 57–64

    Article  Google Scholar 

  181. Cozzens M, Wang D. The general channel assignment problem. Congr Numer, 1984, 41: 115–129

    MathSciNet  Google Scholar 

  182. Zhang L Q, Feng J E. Mix-valued logic-based formation control. Int J Control, 2013, 86: 1191–1199

    Article  MathSciNet  MATH  Google Scholar 

  183. Pukdeboon C, Zinober A. Control Lyapunov function optimal sliding mode controllers for attitude tracking of spacecraft. J Franklin Inst, 2012, 349: 456–475

    Article  MathSciNet  MATH  Google Scholar 

  184. Sharma R, Tewari A. Optimal nonlinear tracking of spacecraft attitude maneuvers. IEEE Trans Control Syst Technol, 2004, 12: 677–682

    Article  Google Scholar 

  185. Zhang Z, Zhang Z X, Zhang H. Decentralized robust attitude tracking control for spacecraft networks under unkonwn ineritia mtrices. Neurocomputing, 2015, 165: 202–210

    Article  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61374065, 61374025, 61503225), Natural Science Foundation of Shandong Province (Grant No. ZR2015FQ003), and Natural Science Fund for Distinguished Young Scholars of Shandong Province (Grant No. JQ201613).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Haitao Li & Guodong Zhao

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Min Meng

  3. School of Mathematics, Shandong University, Jinan, 250100, China

    June Feng

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  1. Haitao Li
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  2. Guodong Zhao
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  3. Min Meng
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  4. June Feng
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Correspondence to Haitao Li.

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Li, H., Zhao, G., Meng, M. et al. A survey on applications of semi-tensor product method in engineering. Sci. China Inf. Sci. 61, 010202 (2018). https://doi.org/10.1007/s11432-017-9238-1

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