Fixed-time synchronization of semi-Markovian jumping neural networks with time-varying delays. (English) Zbl 1446.93016
Summary: This paper is concerned with the global fixed-time synchronization issue for semi-Markovian jumping neural networks with time-varying delays. A novel state-feedback controller, which includes integral terms and time-varying delay terms, is designed to realize the fixed-time synchronization goal between the drive system and the response system. By applying the Lyapunov functional approach and matrix inequality analysis technique, the fixed-time synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results.
MSC:
| 93B12 | Variable structure systems |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 60J74 | Jump processes on discrete state spaces |
| 93E15 | Stochastic stability in control theory |
References:
| [1] | Nitta, T.: Orthogonality of decision boundaries in complex-valued neural networks. Neural Comput. 16, 73-97 (2004) · Zbl 1084.68105 · doi:10.1162/08997660460734001 |
| [2] | Yu, D., Deng, L., Seide, F.: The deep tensor neural network with applications to large vocabulary speech recognition. IEEE Trans. Audio Speech Lang. Process. 21, 388-396 (2012) · doi:10.1109/TASL.2012.2227738 |
| [3] | Wang, D.: Pattern recognition: neural networks in perspective. IEEE Expert 8, 52-60 (2002) · doi:10.1109/64.223991 |
| [4] | Abdurahman, A., Jiang, H., Teng, Z.: Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Netw. 69, 20-28 (2015) · Zbl 1398.34107 · doi:10.1016/j.neunet.2015.04.015 |
| [5] | Yu, J., Hu, C., Jiang, H.: Projective synchronization for fractional neural networks. Neural Netw. 49, 87-95 (2014) · Zbl 1296.34133 · doi:10.1016/j.neunet.2013.10.002 |
| [6] | Ying, W., Yan, J., Cui, B.: Lag synchronization of neural network and its application in secure communication. Appl. Res. Comput. 27, 3456-3457 (2010) |
| [7] | Jun, D., Chen, A.: Exponential synchronization of a class of neural network on time scales. J. Xiangnan Univ. 29, 6-12 (2008) |
| [8] | Li, H., Liao, H., Huang, H.: Synchronization of uncertain chaotic systems based on neural network and sliding mode control. Acta Phys. Sin. 60, 020512 (2011) |
| [9] | Hu, J., Cao, J., Alofi, A.: Pinning synchronization of coupled inertial delayed neural networks. Cogn. Neurodyn. 9, 341-350 (2015) · doi:10.1007/s11571-014-9322-0 |
| [10] | Lang, J., Zhang, Y., Zhang, B.: Event-Triggered Network-Based Synchronization of Delayed Neural Networks. Elsevier, Amsterdam (2016) |
| [11] | Michalak, A., Nowakowski, A.: Finite-time stability and finite-time synchronization of neural network-dual approach. J. Franklin Inst. 354, 8513-8528 (2017) · Zbl 1380.93275 · doi:10.1016/j.jfranklin.2017.08.054 |
| [12] | Hao, Z., Wang, X., Lin, X.: Synchronization of complex-valued neural network with sliding mode control. J. Franklin Inst. 353, 345-358 (2016) · Zbl 1395.93148 · doi:10.1016/j.jfranklin.2015.11.014 |
| [13] | Peng, X., Wu, H., Song, K.: Non-fragile chaotic synchronization for discontinuous neural networks with time-varying delays and random feedback gain uncertainties. Neurocomputing 273, 89-100 (2018) · doi:10.1016/j.neucom.2017.08.024 |
| [14] | Chen, W., Lu, X., Zheng, W.: Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks. IEEE Trans. Neural Netw. Learn. Syst. 26, 734-748 (2017) · doi:10.1109/TNNLS.2014.2322499 |
| [15] | Hu, C., Yu, J., Jiang, H.: Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control. Chaos 20, 023108 (2010) · Zbl 1311.92017 · doi:10.1063/1.3391900 |
| [16] | Zhao, H., Li, L., Peng, H.: Finite-time robust synchronization of memristive neural network with perturbation. Neural Process. Lett. 47, 509-533 (2018) · doi:10.1007/s11063-017-9681-8 |
| [17] | Shen, J., Cao, J.: Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn. Neurodyn. 5, 373-385 (2011) · doi:10.1007/s11571-011-9163-z |
| [18] | Huang, D., Jiang, M., Jian, J.: Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control. Neurocomputing 266, 527-539 (2017) · doi:10.1016/j.neucom.2017.05.075 |
| [19] | Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57, 2016-2110 (2012) · Zbl 1369.93128 · doi:10.1109/TAC.2011.2179869 |
| [20] | Hu, C., Yu, J., Chen, Z.: Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Netw. 89, 74-83 (2017) · Zbl 1441.93279 · doi:10.1016/j.neunet.2017.02.001 |
| [21] | Khanzadeh, A., Pourgholi, M.: Fixed-time sliding mode controller design for synchronization of complex dynamical networks. Nonlinear Dyn. 88, 2637-2649 (2017) · Zbl 1398.93276 · doi:10.1007/s11071-017-3400-x |
| [22] | Zuo, Z.: Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl. 9, 545-552 (2014) · doi:10.1049/iet-cta.2014.0202 |
| [23] | Ding, X., Cao, J., Alsaedi, A.: Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions. Neural Netw. 90, 42-55 (2017) · Zbl 1439.93015 · doi:10.1016/j.neunet.2017.03.006 |
| [24] | Wang, L., Zeng, Z., Hu, J.: Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations. Neural Netw. 87, 122-131 (2017) · Zbl 1440.93101 · doi:10.1016/j.neunet.2016.12.006 |
| [25] | Cao, J., Li, R.: Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci. China Inf. Sci. 60, 032201 (2017) · doi:10.1007/s11432-016-0555-2 |
| [26] | Wei, R., Cao, J., Alsaedi, A.: Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays. Cogn. Neurodyn. 12, 121-134 (2018) · doi:10.1007/s11571-017-9455-z |
| [27] | Chen, C., Li, L., Peng, H.: Fixed-time synchronization of memristor-based BAM neural networks with time-varying discrete delay. Neural Netw. 96, 47-54 (2017) · Zbl 1441.93263 · doi:10.1016/j.neunet.2017.08.012 |
| [28] | Li, T., Song, A., Fei, S.: Synchronization control of chaotic neural networks with time-varying and distributed delays. Nonlinear Anal. 71, 2372-2384 (2009) · Zbl 1171.34049 · doi:10.1016/j.na.2009.01.079 |
| [29] | Wu, H., Zhang, H., Li, R.: Finite-time synchronization of chaotic neural networks with mixed time-varying delays and stochastic disturbance. Memet. Comput. 7, 231-241 (2015) · doi:10.1007/s12293-014-0150-x |
| [30] | Ren, H., Deng, F., Peng, Y.: Finite time synchronization of Markovian jumping stochastic complex dynamical systems with mix delays via hybrid control strategy. Neurocomputing 272, 683-693 (2018) · doi:10.1016/j.neucom.2017.08.013 |
| [31] | Xiong, J., Lam, J.: Robust H2 control of Markovian jumping systems with uncertain switching probabilities. Int. J. Syst. Sci. 40, 255-265 (2009) · Zbl 1167.93335 · doi:10.1080/00207720802300347 |
| [32] | Chandrasekar, A., Rakkiyappan, R., Rihan, F.: Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control. Neurocomputing 133, 385-398 (2014) · doi:10.1016/j.neucom.2013.12.039 |
| [33] | Wu, H., Wang, L., Wang, Y., Niu, P., Fang, B.: Exponential state estimation for Markovian jumping neural networks with mixed time-varying delays and discontinuous activation functions. Int. J. Mach. Learn. Cybern. 7, 641-652 (2016) · doi:10.1007/s13042-015-0447-1 |
| [34] | Shen, H., Park, J., Wu, Z.: Finite time \(H∞H_{\infty}\) synchronization for complex networks with semi-Markov jump topology. Commun. Nonlinear Sci. Numer. Simul. 24, 40-51 (2015) · Zbl 1440.93074 · doi:10.1016/j.cnsns.2014.12.004 |
| [35] | Pradeep, C., Yang, C., Murugesu, R., Rakkiyappand, R.: An event-triggered synchronization of semi-Markov jump neural networks with time-varying delays based on generalized free-weighting-matrix approach. Math. Comput. Simul. (2017). https://doi.org/10.1016/j.matcom.2017.11.001 · Zbl 1540.34103 · doi:10.1016/j.matcom.2017.11.001 |
| [36] | Huang, J., Shi, Y.: Stochastic stability and robust stabilization of semi-Markov jump linear systems. Int. J. Robust Nonlinear Control 23, 2028-2043 (2013) · Zbl 1278.93286 · doi:10.1002/rnc.2862 |
| [37] | Liu, X., Yu, X.: Finite-time \(H∞H_{\infty}\) control for linear systems with semi-Markovian switching. Nonlinear Dyn. 85, 1-12 (2016) · doi:10.1007/s11071-016-2671-y |
| [38] | Li, F., Shi, P., Wu, L.: State estimation and sliding mode control for semi-Markovian jump systems. Automatica 51, 385-393 (2015) · Zbl 1309.93157 · doi:10.1016/j.automatica.2014.10.065 |
| [39] | Huang, J.; Shi, Y., Stochastic stability of semi-Markov jump linear systems: an LMI approach, No. 413, 4668-4673 (2015), Los Alamitos |
| [40] | Xiong, J., Lam, J.: Robust H2 control of Markovian jump systems with uncertain switching probabilities. Int. J. Syst. Sci. 40, 255-265 (2009) · Zbl 1167.93335 · doi:10.1080/00207720802300347 |
| [41] | Hardy, G., Littlewood, J., Polya, G.: Inequalities. Cambridge Mathematical Library, Cambridge (1934) · Zbl 0010.10703 |
| [42] | Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57, 2106-2110 (2012) · Zbl 1369.93128 · doi:10.1109/TAC.2011.2179869 |
| [43] | Levant, A., On fixed and finite time stability in sliding mode control, 4260-4265 (2013), Los Alamitos |
| [44] | Tang, Y.: Terminal sliding mode control for rigid robots. Automatica 34, 51-56 (1998) · Zbl 0908.93042 · doi:10.1016/S0005-1098(97)00174-X |
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.
