CLC number: O157.5
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2020-01-06
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Xiang-shan Kong, Shu-ling Wang, Hai-tao Li, Fuad E. Alsaadi. New developments in control design techniques of logical control networks[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 220-233.
@article{title="New developments in control design techniques of logical control networks",
author="Xiang-shan Kong, Shu-ling Wang, Hai-tao Li, Fuad E. Alsaadi",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="21",
number="2",
pages="220-233",
year="2020",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1900397"
}
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Abstract: The control design problem plays a fundamental role in the study of logical control networks (LCNs). This paper presents a detailed survey on new developments in control design techniques of LCNs. First, some preliminary results on the semi-tensor product method and LCNs are reviewed. Then, we move on to some new developments for control design techniques of LCNs, including the reachable set approach, the pinning control technique, the control Lyapunov function approach, the event-triggered control technique, and the sampled-data control technique. Finally, an illustrative example is given to demonstrate the effectiveness of these techniques.
[1]Åström KJ, Bernhardsson B, 1999. Comparison of periodic and event based sampling for first order stochastic systems. Proc 14th IFAC World Congress, p.5006-5011.
[2]Chen HW, Liang JL, 2017. Output regulation of Boolean control networks with stochastic disturbances. IET Contr Theory Appl, 11(13):2097-2103.
[3]Chen HW, Liang JL, Wang ZD, 2016. Pinning controllability of autonomous Boolean control networks. Sci China Inform Sci, 59(7):070107.
[4]Cheng DZ, Qi HS, Li ZQ, 2011a. Analysis and Control of Boolean Networks: a Semi-tensor Product Approach. Springer, London, UK.
[5]Cheng DZ, Qi HS, Li ZQ, et al., 2011b. Stability and stabilization of Boolean networks. Int J Rob Nonl Contr, 21(2):134-156.
[6]Cheng DZ, Feng JE, Lv HL, 2012. Solving fuzzy relational equations via semitensor product. IEEE Trans Fuzzy Syst, 20(2):390-396.
[7]Cheng DZ, Qi HS, Liu ZQ, 2018. From STP to game-based control. Sci China Inform Sci, 61(1):010201.
[8]Ding XY, Li HT, 2019. Optimal control of random evolutionary Boolean games. Int J Contr, online.
[9]Ding XY, Li HT, Yang QQ, et al., 2017. Stochastic stability and stabilization of n-person random evolutionary Boolean games. Appl Math Comput, 306:1-12.
[10]Ding XY, Li HT, Wang SL, 2018. Set stability and synchronization of logical networks with probabilistic time delays. J Franklin Inst, 355(15):7735-7748.
[11]Ding XY, Li HT, Alsaadi FE, 2019. Regulation of game result for n-person random evolutionary Boolean games. Asian J Contr, online.
[12]Ding Y, Guo YQ, Xie YF, et al., 2017. Time-optimal state feedback stabilization of switched Boolean control networks. Neurocomputing, 237:265-271.
[13]Fan HB, Feng JE, Meng M, et al., 2018. General decomposition of fuzzy relations: semi-tensor product approach. Fuzzy Set Syst, online.
[14]Fornasini E, Valcher MM, 2013. On the periodic trajectories of {Boolean} control networks. Automatica, 49(5):1506-1509.
[15]Fornasini E, Valcher ME, 2016. Recent developments in Boolean networks control. J Contr Dec, 3(1):1-18.
[16]Goebel R, Prieur C, Teel AR, 2009. Smooth patchy control Lyapunov functions. Automatica, 45(3):675-683.
[17]Guo YQ, Wang P, Gui WH, et al., 2015. Set stability and set stabilization of Boolean control networks based on invariant subsets. Automatica, 61:106-112.
[18]Karafyllis I, Jiang ZP, 2013. Global stabilization of nonlinear systems based on vector control Lyapunov functions. IEEE Trans Autom Contr, 58(10):2550-2562.
[19]Lee TH, Park JH, 2017. Improved criteria for sampled-data synchronization of chaotic Lur’e systems using two new approaches. Nonl Anal Hybr Syst, 24:132-145.
[20]Lee TH, Park JH, Kwon OM, et al., 2013. Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neur Netw, 46:99-108.
[21]Li BW, Liu Y, Kou KI, et al., 2018. Event-triggered control for the disturbance decoupling problem of Boolean control networks. IEEE Trans Cybern, 48(9):2764-2769.
[22]Li BW, Lu JQ, Zhong J, et al., 2019a. Fast-time stability of temporal Boolean networks. IEEE Trans Neur Netw Learn Syst, 30(8):2285-2294.
[23]Li BW, Lu JQ, Liu Y, et al., 2019b. The outputs robustness of Boolean control networks via pinning control. IEEE Trans Contr Netw Syst, online.
[24]Li BW, Lou JG, Liu Y, et al., 2019c. Robust invariant set analysis of Boolean networks. Complexity, 2019: 2731395.
[25]Li FF, 2016a. Feedback control design for the complete synchronisation of two coupled Boolean networks. Int J Syst Sci, 47(12):2996-3003.
[26]Li FF, 2016b. Pinning control design for the stabilization of Boolean networks. IEEE Trans Neur Netw Learn Syst, 27(7):1585-1590.
[27]Li FF, 2016c. Pinning control design for the synchronization of two coupled Boolean networks. IEEE Trans Circ Syst, 63(3):309-313.
[28]Li FF, 2018. Stability of Boolean networks with delays using pinning control. IEEE Trans Contr Netw Syst, 5(1): 179-185.
[29]Li FF, Sun JT, 2012. Stability and stabilization of Boolean networks with impulsive effects. Syst Contr Lett, 61(1): 1-5.
[30]Li FF, Tang Y, 2017. Set stabilization for switched Boolean control networks. Automatica, 78:223-230.
[31]Li FF, Xie LH, 2019. Set stabilization of probabilistic Boolean networks using pinning control. IEEE Trans Neur Netw Learn Syst, 30(8):2555-2561.
[32]Li FF, Yan HC, Karimi HR, 2018. Single-input pinning controller design for reachability of Boolean networks. IEEE Trans Neur Netw Learn Syst, 29(7):3264-3269.
[33]Li H, Li Y, Wang S, 2019. Recent development on analysis and control of finite-value dynamic systems. J Shandong Norm Univ Nat Sci, in press (in Chinese).
[34]Li HT, Ding XY, 2019. A control Lyapunov function approach to feedback stabilization of logical control networks. SIAM J Contr Optim, 57(2):810-831.
[35]Li HT, Wang YZ, 2013. Output feedback stabilization control design for Boolean control networks. Automatica, 49(12):3641-3645.
[36]Li HT, Wang YZ, 2016a. Minimum-time state feedback stabilization of constrained Boolean control networks. Asian J Contr, 18(5):1688-1697.
[37]Li HT, Wang YZ, 2016b. Output tracking of switched Boolean networks under open-loop/closed-loop switching signals. Nonl Anal Hybr Syst, 22:137-146.
[38]Li HT, Wang YZ, 2016c. Robust stability and stabilisation of Boolean networks with disturbance inputs. Int J Syst Sci, 48(4):750-756.
[39]Li HT, Wang YZ, 2017a. Further results on feedback stabilization control design of Boolean control networks. Automatica, 83:303-308.
[40]Li HT, Wang YZ, 2017b. Lyapunov-based stability and construction of Lyapunov functions for Boolean networks. SIAM J Contr Optim, 55(6):3437-3457.
[41]Li HT, Xiao XF, Lei XY, et al., 2013a. Second-order consensus seeking in multi-agent systems with nonlinear dynamics over random switching directed networks. IEEE Trans Circ Syst, 60(6):1595-1607.
[42]Li HT, Wang YZ, Liu ZB, 2013b. Simultaneous stabilization for a set of Boolean control networks. Syst Contr Lett, 62(12):1168-1174.
[43]Li HT, Wang YZ, Liu ZB, 2014. Stability analysis for switched Boolean networks under arbitrary switching signals. IEEE Trans Autom Contr, 59(7):1978-1982.
[44]Li HT, Wang YZ, Xie LH, 2015. Output tracking control of Boolean control networks via state feedback: constant reference signal case. Automatica, 59:54-59.
[45]Li HT, Wang YZ, Guo PL, 2016. State feedback based output tracking control of probabilistic Boolean networks. Inform Sci, 349-350:1-11.
[46]Li HT, Wang YZ, Guo PL, 2017a. Output reachability analysis and output regulation control design of Boolean control networks. Sci China Inform Sci, 60(2):022202.
[47]Li HT, Xie LH, Wang YZ, 2017b. Output regulation of Boolean control networks. IEEE Trans Autom Contr, 62(6):2993-2998.
[48]Li HT, Song PP, Yang QQ, 2017c. Pinning control design for robust output tracking of k-valued logical networks. J Franklin Inst, 354(7):3039-3053.
[49]Li HT, Ding XY, Alsaedi A, et al., 2017d. Stochastic set stabilisation of n-person random evolutionary Boolean games and its applications. IET Contr Theory Appl, 11(13):2152-2160.
[50]Li HT, Zhao GD, Meng M, et al., 2018a. A survey on applications of semi-tensor product method in engineering. Sci China Inform Sci, 61(1):010202.
[51]Li HT, Ding XY, Yang QQ, et al., 2018b. Algebraic formulation and Nash equilibrium of competitive diffusion games. Dynam Game Appl, 8(2):423-433.
[52]Li HT, Zheng YT, Alsaadi FE, 2019a. Algebraic formulation and topological structure of Boolean networks with state-dependent delay. J Comput Appl Math, 350:87-97.
[53]Li HT, Xu XJ, Ding XY, 2019b. Finite-time stability analysis of stochastic switched Boolean networks with impulsive effect. Appl Math Comput, 347:557-565.
[54]Li JN, Modares H, Chai TY, et al., 2017. Off-policy reinforcement learning for synchronization in multiagent graphical games. IEEE Trans Neur Netw Learn Syst, 28(10):2434-2445.
[55]Li R, Yang M, Chu TG, 2013. State feedback stabilization for Boolean control networks. IEEE Trans Autom Contr, 58(7):1853-1857.
[56]Li R, Yang M, Chu TG, 2014. State feedback stabilization for probabilistic Boolean networks. Automatica, 50(4):1272-1278.
[57]Li XD, Shen JH, Akca H, et al., 2015. LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter. Appl Math Comput, 250:798-804.
[58]Li XD, Li HT, Zhao GD, 2019a. Function perturbation impact on feedback stabilization of Boolean control networks. IEEE Trans Neur Netw Learn Syst, 30(8):2548-2554.
[59]Li XD, Yang XY, Huang TW, 2019b. Persistence of delayed cooperative models: impulsive control method. Appl Math Comput, 342:130-146.
[60]Li XH, Lu JQ, Chen XY, et al., 2018. Robust output tracking of delayed Boolean networks under pinning control. IEEE Trans Circ Syst, 65(9):1249-1253.
[61]Li YL, Li HT, Sun WW, 2018a. Event-triggered control for robust set stabilization of logical control networks. Automatica, 95:556-560.
[62]Li YL, Li HT, Xu XJ, et al., 2018b. Semi-tensor product approach to minimal-agent consensus control of networked evolutionary games. IET Contr Theory Appl, 12(16):2269-2275.
[63]Li YL, Li HT, Duan PY, 2018c. Synchronization of switched logical control networks via event-triggered control. J Franklin Inst, 355(12):5203-5216.
[64]Li YL, Li HT, Wang SL, 2019. Constrained sampled-data reachability and stabilization of logical control networks. IEEE Trans Circ Syst, 66(12):2002-2006.
[65]Li YY, Li BW, Liu Y, et al., 2018. Set stability and stabilization of switched Boolean networks with state-based switching. IEEE Access, 6:35624-35630.
[67]Liang S, Zhao GD, Li HT, et al., 2019. Structural stability analysis of gene regulatory networks modeled by Boolean networks. Math Meth Appl Sci, 42(7):2221-2230.
[68]Lin L, Zhu SY, Liu Y, et al., 2019. Output regulation of Boolean control networks with nonuniform sampled-data control. IEEE Access, 7:50691-50696.
[69]Liu JY, Liu Y, Guo YQ, et al., 2019. Sampled-data state-feedback stabilization of probabilistic Boolean control networks: a control Lyapunov function approach. IEEE Trans Cybern, online.
[70]Liu RJ, Lu JQ, Lou JG, et al., 2017. Set stabilization of Boolean networks under pinning control strategy. Neurocomputing, 260:142-148.
[71]Liu RJ, Lu JQ, Liu Y, et al., 2018. Delayed feedback control for stabilization of Boolean control networks with state delay. IEEE Trans Neur Netw Learn Syst, 29(7):3283-3288.
[72]Liu RJ, Lu JQ, Zheng WX, et al., 2019. Output feedback control for set stabilization of Boolean control networks. IEEE Trans Neur Netw Learn Syst, online.
[73]Liu S, Li T, Xie LH, et al., 2013. Continuous-time and sampled-data-based average consensus with logarithmic quantizers. Automatica, 49(11):3329-3336.
[74]Liu Y, Lu JQ, Wu B, 2014. Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks. ESAIM Contr Optim Calc Var, 20(1):158-173.
[75]Liu Y, Chen HW, Lu JQ, et al., 2015. Controllability of probabilistic Boolean control networks based on transition probability matrices. Automatica, 52:340-345.
[76]Liu Y, Li BW, Lou JG, 2016a. Disturbance decoupling of singular Boolean control networks. IEEE/ACM Trans Comput Biol Bioinform, 13(6):1194-1200.
[77]Liu Y, Sun LJ, Lu JQ, et al., 2016b. Feedback controller design for the synchronization of Boolean control networks. IEEE Trans Neur Netw Learn Syst, 27(9):1991-1996.
[78]Liu Y, Cao JD, Sun LJ, et al., 2016c. Sampled-data state feedback stabilization of Boolean control networks. Neur Comput, 28(4):778-799.
[79]Liu Y, Li BW, Chen HW, et al., 2017a. Function perturbations on singular Boolean networks. Automatica, 84:36-42.
[80]Liu Y, Li BW, Lu JQ, et al., 2017b. Pinning control for the disturbance decoupling problem of Boolean networks. IEEE Trans Autom Contr, 62(12):6595-6601.
[81]Liu Y, Cao JD, Li BW, et al., 2018. Normalization and solvability of dynamic-algebraic Boolean networks. IEEE Trans Neur Netw Learn Syst, 29(7):3301-3306.
[82]Liu Y, Tong LY, Lou JG, et al., 2019a. Sampled-data control for the synchronization of Boolean control networks. IEEE Trans Cybern, 49(2):726-732.
[83]Liu Y, Wang LQ, Lu JQ, et al., 2019b. Sampled-data stabilization of probabilistic Boolean control networks. Syst Contr Lett, 124:106-111.
[84]Liu YS, Zheng YT, Li HT, et al., 2018. Control design for output tracking of delayed Boolean control networks. J Comput Appl Math, 327:188-195.
[85]Liu ZB, Wang Y, Li H, 2014. New approach to derivative calculation of multi-valued logical functions with application to fault detection. IET Contr Theory Appl, 8(8): 554-560.
[86]Lu JQ, Zhong J, Ho DWC, et al., 2016a. On controllability of delayed Boolean control networks. SIAM J Contr Optim, 54(2):475-494.
[87]Lu JQ, Zhong J, Huang C, et al., 2016b. On pinning controllability of Boolean control networks. IEEE Trans Autom Contr, 61(6):1658-1663.
[88]Lu JQ, Li HT, Liu Y, et al., 2017. Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems. IET Contr Theory Appl, 11(13):2040-2047.
[89]Lu JQ, Li ML, Liu Y, et al., 2018a. Nonsingularity of Grain-like cascade FSRs via semi-tensor product. Sci China Inform Sci, 61(1):010204.
[90]Lu JQ, Sun LJ, Liu Y, et al., 2018b. Stabilization of Boolean control networks under aperiodic sampled-data control. SIAM J Contr Optim, 56(6):4385-4404.
[91]Lu JQ, Li ML, Huang TW, et al., 2018c. The transformation between the Galois NLFSRs and the Fibonacci NLFSRs via semi-tensor product of matrices. Automatica, 96:393-397.
[92]Lu YY, Zhang W, 2017. A piecewise smooth control-Lyapunov function framework for switching stabilization. Automatica, 76:258-265.
[93]Lukk M, Kapushesky M, Nikkilä J, et al., 2010. A global map of human gene expression. Nat Biotechnol, 28(4):322-324.
[94]Mao Y, Wang LQ, Liu Y, et al., 2018. Stabilization of evolutionary networked games with length-r information. Appl Math Comput, 337:442-451.
[95]Moraga C, Trillas E, Guadarrama S, 2003. Multiple-valued logic and artificial intelligence fundamentals of fuzzy control revisited. Artif Intell Rev, 20(3-4):169-197.
[96]Mu NK, Liao XF, Huang TW, 2015. Leader-following consensus in second-order multiagent systems via event-triggered control with nonperiodic sampled data. IEEE Trans Circ Syst, 62(10):1007-1011.
[97]Müller FJ, Schuppert A, 2011. Few inputs can reprogram biological networks. Nature, 478(7369):E4.
[98]Müller FJ, Schuldt BM, Williams R, et al., 2011. A bioinformatic assay for pluripotency in human cells. Nat Meth, 8(4):315-317.
[99]Postoyan R, Tabuada P, NešićD, et al., 2015. A framework for the event-triggered stabilization of nonlinear systems. IEEE Trans Autom Contr, 60(4):982-996.
[100]Rosin DP, Rontani D, Gauthier DJ, et al., 2013. Control of synchronization patterns in neural-like Boolean networks. Phys Rev Lett, 110(5):104102.
[101]Sanfelice RG, 2013. On the existence of control Lyapunov functions and state-feedback laws for hybrid systems. IEEE Trans Autom Contr, 58(12):3242-3248.
[102]Sun LJ, Lu JQ, Ching WK, 2020. Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable. Front Inform Technol Electron Eng, 21(2):260-267.
[103]Tong LY, Liu Y, Alsaadi FE, et al., 2017. Robust sampled-data control invariance for Boolean control networks. J Franklin Inst, 354(15):7077-7087.
[104]Tong LY, Liu Y, Li YY, et al., 2018a. Robust control invariance of probabilistic Boolean control networks via event-triggered control. IEEE Access, 6:37767-37774.
[105]Tong LY, Liu Y, Lou JG, et al., 2018b. Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks. Appl Math Comput, 332:263-275.
[106]Tong LY, Liang JL, Chen HW, 2019. State feedback controller design for anti-synchronization of Boolean control networks: an event-based idea. Asian J Contr, online.
[107]Vaidya U, Mehta PG, Shanbhag UV, 2010. Nonlinear stabilization via control Lyapunov measure. IEEE Trans Autom Contr, 55(6):1314-1328.
[108]Veliz-Cuba A, Stigler B, 2011. Boolean models can explain bistability in the lac operon. J Comput Biol, 18(6):783-794.
[109]Vinodkumar A, Senthilkumar T, Li XD, 2018. Robust exponential stability results for uncertain infinite delay differential systems with random impulsive moments. Adv Differ Equat, 2018:39.
[110]Wang B, Feng JE, 2019. On detectability of probabilistic Boolean networks. Inform Sci, 483:383-395.
[111]Wang JY, Feng JW, Xu C, et al., 2016. The synchronization of instantaneously coupled harmonic oscillators using sampled data with measurement noise. Automatica, 66:155-162.
[112]Wang LQ, Liu Y, Wu ZG, et al., 2019. Stabilization and finite-time stabilization of probabilistic Boolean control networks. IEEE Trans Syst Man Cybern Syst, online.
[113]Wang SL, Li HT, 2019. Column stacking approach to resolution of systems of fuzzy relational inequalities. J Franklin Inst, 356(6):3314-3332.
[114]Wang YH, Cheng DZ, 2017. Stability and stabilization of a class of finite evolutionary games. J Franklin Inst, 354(3):1603-1617.
[115]Wu YQ, Meng XY, Xie LH, et al., 2017. An input-based triggering approach to leader-following problems. Automatica, 75:221-228.
[116]Wu ZG, Shi P, Su HY, et al., 2014. Local synchronization of chaotic neural networks with sampled-data and saturating actuators. IEEE Trans Cybern, 44(12):2635-2645.
[117]Xu XJ, Li HT, Li YL, et al., 2018a. Output tracking control of Boolean control networks with impulsive effects. Math Meth Appl Sci, 41(4):1554-1564.
[118]Xu XJ, Liu YS, Li HT, et al., 2018b. Robust set stabilization of Boolean control networks with impulsive effects. Nonl Anal Model Contr, 23(4):553-567.
[119]Xu XJ, Liu YS, Li HT, et al., 2018c. Synchronization of switched Boolean networks with impulsive effects. Int J Biomath, 11(6):1850080.
[120]Yang JJ, Lu JQ, Li LL, et al., 2019. Event-triggered control for the synchronization of Boolean control networks. Nonl Dynam, 96(2):1335-1344.
[121]Yang JJ, Lu JQ, Lou JG, et al., 2020. Synchronization of drive-response Boolean control networks with impulsive disturbances. Appl Math Comput, 364:124679.
[122]Yang QQ, Li HT, Liu YS, 2016. Pinning control design for feedback stabilization of constrained Boolean control networks. Adv Differ Equat, 2016:182.
[123]Yang QQ, Li HT, Song PP, et al., 2017. Global convergence of serial Boolean networks based on algebraic representation. J Differ Equat Appl, 23(3):633-647.
[124]Yu YY, Feng JE, Wang B, et al., 2018. Sampled-data controllability and stabilizability of Boolean control networks: nonuniform sampling. J Franklin Inst, 335(12):5324-5335.
[125]Yu YY, Meng M, Feng JE, et al., 2019a. An adjoint network approach to design stabilizable switching signals of switched Boolean networks. Appl Math Comput, 357:12-22.
[126]Yu YY, Feng JE, Pan JF, et al., 2019b. Block decoupling of Boolean control networks. IEEE Trans Autom Contr, 64(8):3129-3140.
[127]Yu YY, Wang B, Feng JE, 2019c. Input observability of Boolean control networks. Neurocomputing, 333:22-28.
[128]Zhang LQ, Feng JE, Feng XH, et al., 2014. Further results on disturbance decoupling of mix-valued logical networks. IEEE Trans Autom Contr, 59(6):1630-1634.
[129]Zhao Y, Ghosh BK, Cheng DZ, 2016. Control of large-scale Boolean networks via network aggregation. IEEE Trans Neur Netw Learn Syst, 27(7):1527-1536.
[130]Zheng YT, Li HT, Ding XY, et al., 2017. Stabilization and set stabilization of delayed Boolean control mboxnetworks based on trajectory stabilization. J Franklin Inst, 354(17):7812-7827.
[131]Zhong J, Lu JQ, Liu Y, et al., 2014. Synchronization in an array of output-coupled Boolean networks with time delay. IEEE Tran Neur Netw Learn Syst, 25(12):2288-2294.
[132]Zhong J, Lu JQ, Huang TW, et al., 2017a. Controllability and synchronization analysis of identical-hierarchy mixed-valued logical control networks. IEEE Trans Cybern, 47(11):3482-3493.
[133]Zhong J, Ho DWC, Lu JQ, et al., 2017b. Switching-signal-triggered pinning control for output tracking of switched Boolean networks. IET Contr Theory Appl, 11(13):2089-2096.
[134]Zhong J, Ho DWCH, Lu JQ, et al., 2019a. Pinning controllers for activation output tracking of Boolean network under one-bit perturbation. IEEE Trans Cybern, 49(9):3398-3408.
[135]Zhong J, Liu Y, Kou KI, et al., 2019b. On the ensemble controllability of Boolean control networks using STP method. Appl Math Comput, 358:51-62.
[136]Zhong J, Li BW, Liu Y, et al., 2020. Output feedback stabilizer design of Boolean networks based on network structure. Front Inform Technol Electron Eng, 21(2):247-259.
[137]Zhu B, Xia XH, Wu Z, 2016. Evolutionary game theoretic demand-side management and control for a class of networked smart grid. Automatica, 70:94-100.
[138]Zhu QX, Lin W, 2019. Stabilizing Boolean networks by optimal event-triggered feedback control. Syst Contr Lett, 126:40-47.
[139]Zhu QX, Liu Y, Lu JQ, et al., 2018a. Controllability and observability of Boolean control networks via sampled-data control. IEEE Trans Contr Netw Syst, online.
[140]Zhu QX, Liu Y, Lu JQ, et al., 2018b. Observability of Boolean control networks. Sci China Inform Sci, 61(9): 092201.
[141]Zhu QX, Liu Y, Lu JQ, et al., 2018c. On the optimal control of Boolean control networks. SIAM J Contr Optim, 56(2):1321-1341.
[142]Zhu QX, Liu Y, Lu JQ, et al., 2019. Further results on the controllability of Boolean control networks. IEEE Trans Autom Contr, 64(1):440-442.
[143]Zhu SY, Lou JG, Liu Y, et al., 2018a. Event-triggered control for the stabilization of probabilistic Boolean control networks. Complexity, 2018:9259348.
[144]Zhu SY, Liu Y, Lou JG, et al., 2018b. Sampled-data state feedback control for the set stabilization of Boolean control networks. IEEE Trans Syst Man Cybern Syst, online.
[145]Zhu SY, Lu JQ, Ho DWC, 2019. Topological sorting for finite-time stability of probabilistic logical networks. IEEE Trans Circ Syst, online.
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