Stabilization analysis of impulsive state-dependent neural networks with nonlinear disturbance: A quantization approach

Hong, Yaxian ; Bin, Honghua ; Huang, Zhenkun

International Journal of Applied Mathematics and Computer Science, Tome 30 (2020) no. 2, pp. 267-279.

Résumé

In this paper, the problem of feedback stabilization for a class of impulsive state-dependent neural networks (ISDNNs) with nonlinear disturbance inputs via quantized input signals is discussed. By constructing quasi-invariant sets and attracting sets for ISDNNs, we design a quantized controller with adjustable parameters. In combination with a suitable ISS-Lyapunov functional and a hybrid quantized control strategy, we propose novel criteria on input-to-state stability and global asymptotical stability for ISDNNs. Our results complement the existing ones. Numerical simulations are reported to substantiate the theoretical results and effectiveness of the proposed strategy.

Détail

Keywords: state dependent neural network, quantized input, stabilization analysis
Mots-clés : sieć neuronowa, dane wejściowe kwantyzowane, analiza stateczności

Bibliographie

[1] Aubin, J.P. and Cellina, A. (1984). Differential Inclusions: Set-Valued Maps and Viability Theory, Springer-Verlag, Berlin.

[2] Chang, X., Zhang, X. and Yan, L. (2013). Synchronization of complex dynamical networks via sampled-data quantized feedback, 32nd Chinese Control Conference, Xi’an, China, pp. 6531–6536.

[3] Chua, L.C. (1971). Memristor—The missing circuit element, IEEE Transactions on Circuit Theory 18(5): 507–519.

[4] Duan, S., Wang, H., Wang, L., Huang, T. and Li, C. (2017). Impulsive effects and stability analysis on memristive neural networks with variable delays, IEEE Transactions on Neural Networks and Learning Systems 28(2): 476–481.

[5] Fan, Y., Wang, W. and Jiang, X. (2016). Synchronization for chaotic Lur’e systems based on adaptive quantized state measurements control design, 35th Chinese Control Conference, Chengdu, China, pp. 913–915.

[6] Guo, Z., Liu, L. and Wang, J. (2018). Multistability for recurrent neural networks with piecewise-linear radial basis functions and state-dependent switching parameters, IEEE Transactions on Systems, Man and Cybernetics: Systems 30(7): 2052–2066.

[7] Hao, Z., Yan, H., Yang, F. and Chen, Q. (2011). Quantized control design for impulsive fuzzy networked systems, IEEE Transactions on Fuzzy Systems 19(6): 1153–1162.

[8] Hong, Y., Bin, H. and Huang, Z. (2019). Synchronization of state-switching Hopfield-type neural networks: A quantized level set approach, Chaos, Solitons and Fractals 129: 16–24.

[9] Huang, C., Su, R., Cao, J. and Xiao, S. (2019). Asymptotically stable high-order neutral cellular neural networks with proportional delays and d operators, Mathematics and Computers in Simulation 5(155): 41–56.

[10] Huang, Z., Bin, H., Cao, J. and Wang, B. (2018a). Synchronization networks with proportional delays based on a class of q-type allowable time scales, IEEE Transactions on Neural Networks and Learning Systems 29(8): 3418–3428.

[11] Huang, Z., Cao, J. and Raffoul, Y.N. (2018b). Hilger-type impulsive differential inequality and its application to impulsive synchronization of delayed complex networks on time scales, Science China (Information Sciences) 61(7): 244–246.

[12] Lakshmikantham, V., Bainov, D.D. and Simeonov, P.S. (1989). Theory of Impulsive Differential Equations, World Scientific, Singapore.

[13] Qian, Y., Cui, B. and Lou, X. (2012). Quantized feedback control for hybrid impulsive systems, 12th International Conference on Control, Automation and Systems, JeJu Island, South Korea, pp. 1–6.

[14] Sontag, E.D. (2002). Smooth stabilization implies coprime factorization, IEEE Transactions on Automatic Control 34(4): 435–443.

[15] Sun, H., Hou, L., Zong, G. and Yu, X. (2019). Fixed-time attitude tracking control for spacecraft with input quantization, IEEE Transactions on Aerospace and Electronic Systems 55(1): 124–134.

[16] Wan, Y., Cao, J. and Wen, G. (2017). Quantized synchronization of chaotic neural networks with scheduled output feedback control, IEEE Transactions on Neural Networks and Learning Systems 28(11): 2638–2647.

[17] Wang, H., Duan, S., Huang, T., Li, C. and Wang, L. (2016). Novel stability criteria for impulsive memristive neural networks with time-varying delays, Circuits Systems and Signal Processing 35(11): 3935–3956.

[18] Wu, Z.G., Yong, X., Pan, Y.J., Su, H. and Yang, T. (2018). Event-triggered control for consensus problem in multi-agent systems with quantized relative state measurements and external disturbance, IEEE Transactions on Circuits and Systems I: Regular Papers 65(7): 2232–2242.

[19] Xu, D. and Long, S. (2012). Attracting and quasi-invariant sets of non-autonomous neural networks with delays, Neurocomputing 77(1): 222–228.

[20] Yang, D., Qiu, G. and Li, C. (2016). Global exponential stability of memristive neural networks with impulse time window and time-varying delays, Neurocomputing 171: 1021–1026.

[21] Yang, X., Cao, J. and Lu, J. (2011). Synchronization of delayed complex dynamical networks with impulsive and stochastic effects, Nonlinear Analysis Real World Applications 12(4): 2252–2266.

[22] Yang, X., Qiang, S., Cao, J. and Lu, J. (2019). Synchronization of coupled Markovian reaction–diffusion neural networks with proportional delays via quantized control, IEEE Transactions on Neural Networks and Learning Systems 30(3): 951–958.

[23] Yu, J., Cheng, H., Jiang, H. and Teng, Z. (2014). Stabilization of nonlinear systems with time-varying delays via impulsive control, Neurocomputing 125(3): 68–71.

[24] Zhang, G. and Shen, Y. (2015). Novel conditions on exponential stability of a class of delayed neural networks with state-dependent switching, Neural Networks 71: 55–61.

[25] Zhang, W., Yang, S., Li, C. and Li, Z. (2019). Finite-time and fixed-time synchronization of complex networks with discontinuous nodes via quantized control, Neural Processing Letters 6: 1–14.

[26] Zhu, W., Wang, D., Liu, L. and Feng, G. (2018). Event-based impulsive control of continuous-time dynamic systems and its application to synchronization of memristive neural networks, IEEE Transactions on Neural Networks and Learning Systems 29(8): 3599–3609.