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State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays. (English) Zbl 1227.92002

Summary: We investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
15A45 Miscellaneous inequalities involving matrices
60J75 Jump processes (MSC2010)
62M05 Markov processes: estimation; hidden Markov models
65C20 Probabilistic models, generic numerical methods in probability and statistics
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References:

[1] Arik, S., IEEE Trans. Circuits Systems I, 47, 1089 (2000) · Zbl 0992.93080
[2] Joy, M. P., Neural Networks, 13, 613 (2000)
[3] Wang, Z.; Ho, D.; Liu, X., IEEE Trans. Neural Networks, 16, 1, 279 (2005)
[4] Cao, J.; Huang, D.-S.; Qu, Y., Chaos Solitons Fractals, 23, 1, 221 (2005) · Zbl 1075.68070
[5] Cao, J.; Ho, D., Chaos Solitons Fractals, 24, 5, 1317 (2005) · Zbl 1072.92004
[6] Huang, H.; Cao, J., Appl. Math. Comput., 142, 1, 143 (2003) · Zbl 1035.34081
[7] Singh, V., Chaos Solitons Fractals, 29, 2, 470 (2006) · Zbl 1188.34099
[8] Song, Q.; Zhao, Z.; Li, Y., Phys. Lett. A, 335, 2-3, 213 (2005) · Zbl 1123.68347
[9] Song, Q.; Zhao, Z., Chaos Solitons Fractals, 25, 2, 393 (2005) · Zbl 1072.92005
[10] Wang, Z.; Liu, Y.; Liu, X., Phys. Lett. A, 345, 4-6, 299 (2005) · Zbl 1345.92017
[11] Zhao, H., Neural Networks, 17, 47 (2004) · Zbl 1082.68100
[12] Zhao, H., Phys. Lett. A, 336, 331 (2005) · Zbl 1136.34348
[13] Liu, Y.; Wang, Z.; Liu, X., Neural Networks, 19, 5, 667 (2006) · Zbl 1102.68569
[14] Salam, F. M.; Zhang, J., Adaptive neural observer with forward co-state propagation, (Proceedings of the International Joint Conference on Neural Networks (IJCNN ’01), vol. 1. Proceedings of the International Joint Conference on Neural Networks (IJCNN ’01), vol. 1, Washington, USA (2001)), 675-680
[15] Habtom, R.; Litz, L., Estimation of unmeasured inputs using recurrent neural networks and the extended Kalman filter, (Proceedings of the International Conference on Neural Networks, vol. 4. Proceedings of the International Conference on Neural Networks, vol. 4, Houston, USA (1997)), 2067-2071
[16] Elanayar, V.; Shin, Y., IEEE Trans. Neural Networks, 5, 4, 594 (1994)
[17] Huang, H.; Feng, G.; Cao, J., IEEE Trans. Neural Networks, 19, 8, 1329 (2008)
[18] Tino, P.; Cernansky, M.; Benuskova, L., IEEE Trans. Neural Networks, 15, 1, 6 (2004)
[19] Wang, Z.; Liu, Y.; Yu, L.; Liu, X., Phys. Lett. A, 356, 4-5, 346 (2006) · Zbl 1160.37439
[20] Liu, Y.; Wang, Z.; Liu, X., Phys. Lett. A, 372, 22, 3986 (2008) · Zbl 1220.90040
[21] Liu, Y.; Wang, Z.; Liang, J.; Liu, X., IEEE Trans. Systems Man Cybern. Part B, 38, 5, 1314 (2008)
[22] Wang, Z.; Gao, H.; Cao, J.; Liu, X., IEEE Trans. NanoBiosci., 7, 2, 154 (2008)
[23] Wang, Z.; Liu, Y.; Liu, X., Automatica, 44, 5, 1268 (2008) · Zbl 1283.93284
[24] Wang, Z.; Yang, F.; Ho, D. W.C.; Swift, S.; Tucker, A.; Liu, X., IEEE Trans. NanoBiosci., 7, 1, 44 (2008)
[25] Gao, H.; Chen, T., IEEE Trans. Automat. Control, 52, 2, 328 (2007) · Zbl 1366.39011
[26] Gao, H.; Wang, C., Asian J. Control, 7, 2, 81 (2005)
[27] Gao, H.; Wang, C., IEEE Trans. Signal Process., 52, 6, 1631 (2004) · Zbl 1369.93175
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