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

Haitao Li1, Guodong Zhao1, Meng Meng2, Jun-e Feng3
1School of Mathematics and Statistics, Shandong Normal University, Jinan, China
2School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
3School of Mathematics, Shandong University, Jinan, China

Tóm tắt

Từ khóa


Tài liệu tham khảo

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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