Abstract
This paper investigates the global stabilization problem of k-valued logical control networks (KVLCNs) via event-triggered control (ETC), where the control inputs only work at several certain individual states. Compared with traditional state feedback control, the designed ETC approach not only shortens the transient period of logical networks but also decreases the number of controller executions. The content of this paper is divided into two parts. In the first part, a necessary and sufficient criterion is derived for the event-triggered stabilization of KVLCNs, and a construction procedure is developed to design all time-optimal event-triggered stabilizers. In the second part, the switching-cost-optimal event-triggered stabilizer is designed to minimize the number of controller executions. A labeled digraph is obtained based on the dynamic of the overall system. Utilizing this digraph, we formulate a universal and unified procedure called the minimal spanning in-tree algorithm to minimize the triggering event set. Furthermore, we illustrate the effectiveness of obtained results through several numerical examples.
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References
Davidson E H, Rast J P, Oliveri P, et al. A genomic regulatory network for development. Science, 2002, 295: 1669–1678
Liang J L, Lam J, Wang Z D. State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates. Phys Lett A, 2009, 373: 4328–4337
Kauffman S A. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 1969, 22
Goodwin B C. Temporal Organization in Cells: A Dynamic Theory of Cellular Control Processes. London: Academic, 1963
Davidich M I, Bornholdt S. Boolean network model predicts cell cycle sequence of fission yeast. PLoS One, 2008, 3: e1672
Ideker T, Galitski T, Hood L. A new approach to decoding life: systems biology. Annu Rev Genom Hum Genet, 2001, 2: 343–372
Akutsu T, Hayashida M, Ching W K, et al. Control of Boolean networks: hardness results and algorithms for tree structured networks. J Theor Biol, 2007, 244: 670–679
Huang S, Ingber D E. Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks. Exp Cell Res, 2000, 261: 91–103
Cheng D Z, Qi H S, Li Z Q. Analysis and Control of Boolean Networks: A Semi-Tensor Product Approach. Berlin: Springer, 2011
Bof N, Fornasini E, Valcher M E. Output feedback stabilization of Boolean control networks. Automatica, 2015, 57: 21–28
Li R, Yang M, Chu T G. State feedback stabilization for boolean control networks. IEEE Trans Automat Contr, 2013, 58: 1853–1857
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
Wang L Q, Liu Y, Wu Z G, et al. Stabilization and finite-time stabilization of probabilistic Boolean control networks. IEEE Trans Syst Man Cybern Syst, 2019. doi: 10.1109/TSMC.2019.2898880
Li H T, Ding X Y. A control Lyapunov function approach to feedback stabilization of logical control networks. SIAM J Control Opt, 2019, 57: 810–831
Li Y Y, Li B W, Liu Y, et al. Set stability and stabilization of switched Boolean networks with state-based switching. IEEE Access, 2018, 6: 35624–35630
Meng M, Liu L, Feng G. Stability and l1 gain analysis of Boolean networks with Markovian jump parameters. IEEE Trans Automat Contr, 2017, 62: 4222–4228
Li F F, Tang Y. Set stabilization for switched Boolean control networks. Automatica, 2017, 78: 223–230
Li B W, Lou J G, Liu Y, et al. Robust invariant set analysis of Boolean networks. Complexity, 2019, 2019: 1–8
Tong L Y, Liu Y, Li Y Y, et al. Robust control invariance of probabilistic boolean control networks via event-triggered control. IEEE Access, 2018, 6: 37767–37774
Gao Z G, Chen X D, Başar T. Stability structures of conjunctive Boolean networks. Automatica, 2018, 89: 8–20
Liu Y, Cao J D, Wang L Q, et al. On pinning reachability of probabilistic Boolean control networks. Sci China Inf Sci, 2020, 63: 169201
Zhu Q X, Liu Y, Lu J Q, et al. Further results on the controllability of Boolean control networks. IEEE Trans Automat Contr, 2019, 64: 440–442
Zhong J, Liu Y, Kou K I, et al. On the ensemble controllability of Boolean control networks using STP method. Appl Math Comput, 2019, 358: 51–62
Guo Y Q. Observability of Boolean control networks using parallel extension and set reachability. IEEE Trans Neural Netw Learn Syst, 2018, 29: 6402–6408
Li Y Y, Zhong J, Lu J Q, et al. On robust synchronization of drive-response Boolean control networks with disturbances. Math Probl Engin, 2018, 2018: 1737685
Chen H W, Liang J L. Local synchronization of interconnected Boolean networks with stochastic disturbances. IEEE Trans Neural Netw Learn Syst. 2019. doi: 10.1109/TNNLS.2019.2904978
Liu Y, Li B W, Chen H W, et al. Function perturbations on singular Boolean networks. Automatica, 2017, 84: 36–42
Wang S, Feng J E, Yu Y, et al. Further results on dynamic-algebraic Boolean control networks. Sci China Inf Sci, 2019, 62: 012208
Yu Y Y, Feng J E, Pan J F, et al. Block decoupling of Boolean control networks. IEEE Trans Automat Contr, 2019, 64: 3129–3140
Wu Y H, Sun X M, Zhao X D, et al. Optimal control of Boolean control networks with average cost: a policy iteration approach. Automatica, 2019, 100: 378–387
Chen S Q, Wu Y H, Macauley M, et al. Monostability and bistability of Boolean networks using semi-tensor products. IEEE Trans Control Netw Syst, 2018. doi:10.1109/TCNS.2018.2889015
Zhu Q X, Liu Y, Lu J Q, et al. On the optimal control of Boolean control networks. SIAM J Control Opt, 2018, 56: 1321–1341
Lu J Q, Li M L, Huang T W, et al. The transformation between the Galois NLFSRs and the Fibonacci NLFSRs via semi-tensor product of matrices. Automatica, 2018, 96: 393–397
Guo P L, Zhang H X, Alsaadi F E, et al. Semi-tensor product method to a class of event-triggered control for finite evolutionary networked games. IET Control Theor Appl, 2017, 11: 2140–2145
Mao Y, Wang L Q, Liu Y, et al. Stabilization of evolutionary networked games with length-r information. Appl Math Computat, 2018, 337: 442–451
Cao Y, Zhang L Y, Li C Y, et al. Observer-based consensus tracking of nonlinear agents in hybrid varying directed topology. IEEE Trans Cybern, 2017, 47: 2212–2222
Cao Y. Bifurcations in an Internet congestion control system with distributed delay. Appl Math Computat, 2019, 347: 54–63
Cao J D, Guerrini L, Cheng Z S. Stability and Hopf bifurcation of controlled complex networks model with two delays. Appl Math Comput, 2019, 343: 21–29
Liu Y, Li B W, Lu J Q, et al. Pinning control for the disturbance decoupling problem of Boolean networks. IEEE Trans Automat Contr, 2017, 62: 6595–6601
Lu J Q, Sun L J, Liu Y, et al. Stabilization of Boolean control networks under aperiodic sampled-data control. SIAM J Control Opt, 2018, 56: 4385–4404
Heemels W P M H, Johansson K H, Tabuada P. An introduction to event-triggered and self-triggered control. In: Proceedings of IEEE 51st Annual Conference on Decision and Control, Maui, 2012. 3270–3285
Li B W, Liu Y, Kou K I, et al. Event-triggered control for the disturbance decoupling problem of Boolean control networks. IEEE Trans Cybern, 2018, 48: 2764–2769
Li Y L, Li H T, Sun W W. Event-triggered control for robust set stabilization of logical control networks. Automatica, 2018, 95: 556–560
Zhu S Y, Lou J G, Liu Y, et al. Event-triggered control for the stabilization of probabilistic Boolean control networks. Complexity, 2018, 2018: 9259348
Tan X G, Cao J D, Li X D. Consensus of leader-following multiagent systems: a distributed event-triggered impulsive control strategy. IEEE Trans Cybern, 2019, 49: 792–801
Li C J, Yu X H, Yu W W, et al. Distributed event-triggered scheme for economic dispatch in smart grids. IEEE Trans Ind Inf, 2016, 12: 1775–1785
Ljung L, Soderstrom T. Theory and Practice of Recursive Identification. Cambridge: MIT Press, 1983
Liang J L, Chen H W, Liu Y. On algorithms for state feedback stabilization of Boolean control networks. Automatica, 2017, 84: 10–16
Edmonds J. Optimum branchings. J Res Natl Bureau Stan Sect B Math Math Phys, 1967, 71B: 233–240
Acknowledgements
This work was partially supported by National Natural Science Foundation of China (Grant Nos. 11671361, 61833005, 61573096), Natural Science Foundation of Zhejiang Province (Grant No. LD19A010001), Natural Science Foundation of Jiangsu Province (Grant No. BK20170019), and Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (Grant No. BM2017002).
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Zhu, S., Liu, Y., Lou, Y. et al. Stabilization of logical control networks: an event-triggered control approach. Sci. China Inf. Sci. 63, 112203 (2020). https://doi.org/10.1007/s11432-019-9898-3
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DOI: https://doi.org/10.1007/s11432-019-9898-3