Huang, Chi; Lu, Jianquan; Ho, Daniel W. C.; Zhai, Guisheng; Cao, Jinde Stabilization of probabilistic Boolean networks via pinning control strategy. (English) Zbl 1461.93381 Inf. Sci. 510, 205-217 (2020). Summary: The stabilization of probabilistic Boolean networks with pinning control is investigated. Only a part of nodes are chosen to be controlled for the aim of high efficiency. Stabilization with probability one and stabilization in probability are respectively discussed. Since the probability of stabilization is not required to be strict one, stabilization in probability is a more practical extension of the former, which is also proven in this work. Stabilization with probability one needs the target state to be transferred to itself with 100% certainty, while stabilization in probability cannot even guarantee the existence of such a possibility. Thus, stabilization in probability is a different and challenging problem. Some necessary and sufficient conditions are proposed for both types of stabilization via the semi-tensor product of matrices. Based on them, approaches to controller design are also developed. Finally, illustrative examples are provided to demonstrate the effectiveness of the derived results. Cited in 27 Documents MSC: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 93C29 Boolean control/observation systems 93B70 Networked control Keywords:probabilistic Boolean network; stabilization in probability; stabilization with probability one; pinning control PDFBibTeX XMLCite \textit{C. Huang} et al., Inf. Sci. 510, 205--217 (2020; Zbl 1461.93381) Full Text: DOI References: [1] Albert, R.; Othmer, H. G., The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in drosophila melanogaster, J. Theoret. Biol., 223, 1-18 (2003) · Zbl 1464.92108 [2] Arnout, G.; De Man, H. J., The use of threshold functions and Boolean-controlled network elements for macromodeling of LSI circuits, IEEE J. Solid-State Circuits, 13, 326-332 (1978) [3] Bao, G.; Zeng, Z.; Shen, Y., Region stability analysis and tracking control of memristive recurrent neural network, Neural Netw., 98, 51-58 (2018) · Zbl 1436.93114 [4] Chen, H.; Liang, J.; Wang, Z., Pinning controllability of autonomous Boolean control networks, Sci. China Inf. Sci., 59, 070107 (2016) [5] Cheng, D.; Qi, H., Controllability and observability of Boolean control networks, Automatica, 45, 1659-1667 (2009) · Zbl 1184.93014 [6] Cheng, D.; Qi, H.; Li, Z., Analysis and control of Boolean networks: a semi-tensor product approach (2010), Springer Science & Business Media [7] Cheng, D.; Qi, H.; Li, Z.; Liu, J. B., Stability and stabilization of Boolean networks, Int. J. Robust Nonlinear Control, 21, 134-156 (2011) · Zbl 1213.93121 [8] Fan, H.; Feng, J. E.; Meng, M.; Wang, B., General decomposition of fuzzy relations: semi-tensor product approach, Fuzzy Sets Syst. (2018) [9] Fornasini, E.; Valcher, M. E., Optimal control of Boolean control networks, IEEE Trans. Autom. Control, 59, 1258-1270 (2014) · Zbl 1360.93387 [10] Gu, J. W.; Ching, W. K.; Siu, T. K.; Zheng, H., On modeling credit defaults: a probabilistic Booleannetwork approach, Risk Decis. Anal., 4, 119-129 (2013) · Zbl 1294.91182 [11] Guo, Y.; Wang, P.; Gui, W.; Yang, C., Set stability and set stabilization of Booleancontrol networks based on invariant subsets, Automatica, 61, 106-112 (2015) · Zbl 1327.93347 [12] Huang, C.; Wang, W.; Cao, J.; Lu, J., Synchronization-based passivity of partially coupled neural networks with event-triggered communication, Neurocomputing, 319, 134-143 (2018) [13] Kauffman, S. A., Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theoret. Biol., 22, 437-467 (1969) [14] Kobayashi, K.; Hiraishi, K., An integer programming approach to optimal control problems in context-sensitive probabilistic Boolean networks, Automatica, 47, 1260-1264 (2011) · Zbl 1235.93260 [15] Li, F., Pinning control design for the synchronization of two coupled Boolean networks, IEEE Trans. Circuits Syst. II: Express Briefs, 63, 309-313 (2016) [16] Li, H.; Wang, Y., Output feedback stabilization control design for Boolean control networks, Automatica, 49, 3641-3645 (2013) · Zbl 1315.93064 [17] Li, H.; Wang, Y.; Guo, P., State feedback based output tracking control of probabilistic Boolean networks, Inf. Sci., 349, 1-11 (2016) · Zbl 1398.93124 [18] Li, L.; Ho, D. W.; Cao, J.; Lu, J., Pinning cluster synchronization in an array of coupled neural networks under event-based mechanism, Neural Netw., 76, 1-12 (2016) · Zbl 1417.34111 [19] Li, R.; Yang, M.; Chu, T., State feedback stabilization for probabilistic Boolean networks, Automatica, 50, 1272-1278 (2014) · Zbl 1298.93275 [20] Li, Y., Impulsive synchronization of stochastic neural networks via controlling partial states, Neural Process. Lett., 46, 59-69 (2017) [21] Li, Y.; Li, B.; Liu, Y.; Lu, J.; Wang, Z.; Alsaadi, F. E., Set stability and stabilization of switched Booleannetworks with state-based switching, IEEE Access, 6, 35624-35630 (2018) [22] Li, Y.; Liu, R.; Lou, J.; Lu, J.; Wang, Z.; Liu, Y., Output tracking of Boolean control networks driven by constant reference signal, IEEE Access, 7, 112572-112577 (2019) [23] Li, Y.; Lou, J.; Wang, Z.; Alsaadi, F. E., Synchronization of nonlinearly coupled dynamical networks under hybrid pinning impulsive controllers, J. Franklin Inst., 355, 6520-6530 (2018) · Zbl 1398.93144 [24] Lin, G.; Ao, B.; Chen, J.; Wang, W.; Di, Z., Modeling and controlling the two-phase dynamics of the p53 network: a Boolean network approach, New J. Phys., 16, 125010 (2014) [25] Liu, Y.; Chen, H.; Lu, J.; Wu, B., Controllability of probabilistic Boolean control networks based on transition probability matrices, Automatica, 52, 340-345 (2015) · Zbl 1309.93026 [26] Liu, Y.; Li, B.; Lu, J.; Cao, J., Pinning control for the disturbance decoupling problem of Boolean networks, IEEE Trans. Autom. Control, 62, 6595-6601 (2017) · Zbl 1390.93545 [27] Lu, J.; Li, M.; Huang, T.; Liu, Y.; Cao, J., The transformation between the galois NLFSRs and the fibonacci NLFSRs via semi-tensor product of matrices, Automatica, 96, 393-397 (2018) · Zbl 1408.94924 [28] Lu, J.; Sun, L.; Liu, Y.; Ho, D. W.; Cao, J., Stabilization of Boolean control networks under aperiodic sampled-data control, SIAM J. Control Optim., 56, 4385-4404 (2018) · Zbl 1403.93124 [29] Lu, J.; Zhong, J.; Huang, C.; Cao, J., On pinning controllability of Boolean control networks, IEEE Trans. Autom. Control, 61, 1658-1663 (2016) · Zbl 1359.93057 [30] Pal, R.; Datta, A.; Bittner, M. L.; Dougherty, E. R., Intervention in context-sensitive probabilistic Boolean networks, Bioinformatics, 21, 1211-1218 (2004) [31] Rämö, P.; Kesseli, J.; Yli-Harja, O., Stability of functions in Boolean models of gene regulatory networks, Chaos: Interdiscip. J. Nonlinear Sci., 15, 034101 (2005) · Zbl 1144.37401 [32] Rosin, D. P.; Rontani, D.; Gauthier, D. J.; Schöll, E., Control of synchronization patterns in neural-like Boolean networks, Phys. Rev. Lett., 110, 104102 (2013) [33] Shmulevich, I.; Dougherty, E. R.; Kim, S.; Zhang, W., Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks, Bioinformatics, 18, 261-274 (2002) [34] Tong, L.; Liu, Y.; Li, Y.; Lu, J.; Wang, Z.; Alsaadi, F. E., Robust control invariance of probabilistic Booleancontrol networks via event-triggered control, IEEE Access, 6, 37767-37774 (2018) [35] Tournier, L.; Chaves, M., Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics, J. Theoret. Biol., 260, 196-209 (2009) · Zbl 1402.92207 [36] Wang, B.; Feng, J. E., On detectability of probabilistic Boolean networks, Inf. Sci., 483, 383-395 (2019) [37] Williams, P. D.; Pollock, D. D.; Goldstein, R. A., Functionality and the evolution of marginal stability in proteins: inferences from lattice simulations, Evol. Bioinform., 2, 91-101 (2006) [38] Wu, A.; Zeng, Z., Global mittag-leffler stabilization of fractional-order memristive neural networks, IEEE Trans. Neural Netw. Learn.Syst., 28, 206-217 (2017) [39] Yang, J.; Lu, J.; Li, L.; Liu, Y.; Wang, Z.; Alsaadi, F. E., Event-triggered control for the synchronization of Boolean control networks, Nonlinear Dyn., 96, 1335-1344 (2019) · Zbl 1437.93046 [40] Yu, Y.; Feng, J. E.; Pan, J.; Cheng, D., Block decoupling of Boolean control networks, IEEE Trans. Autom. Control, 64, 3129-3140 (2019) · Zbl 1482.93027 [41] Zhang, S.; Ching, W.; Chen, X.; Tsing, N., Generating probabilistic Boolean networks from a prescribed stationary distribution, Inf. Sci., 180, 2560-2570 (2010) · Zbl 1193.92048 [42] Zhang, W.; Zhao, Y.; Sheng, L., Some remarks on stability of stochastic singular systems with state-dependent noise, Automatica, 51, 273-277 (2015) · Zbl 1309.93182 [43] Zhao, Y.; Cheng, D., On controllability and stabilizability of probabilistic Boolean control networks, Sci. China Inf. Sci., 57, 1-14 (2014) · Zbl 1331.93027 [44] Zhong, J.; Ho, D. W.; Lu, J.; Xu, W., Global robust stability and stabilization of Booleannetwork with disturbances, Automatica, 84, 142-148 (2017) · Zbl 1376.93079 [45] Zhong, J.; Li, B.; Liu, Y.; Gui, W., Output feedback stabilizer design of Boolean networks based on network structure, Front. Inf. Technol. Electron.Eng. (2020) [46] Zhu, S.; Lou, J.; Liu, Y.; Li, Y.; Wang, Z., Event-triggered control for the stabilization of probabilistic Boolean control networks, Complexity, 2018, 9259348 (2018) · Zbl 1405.93227 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.