State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays
Abstract
:1. Introduction
2. Preliminaries and Model Descriptions
3. Main Results
4. Numerical Examples
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Sharma, S.; Lingras, P.; Xu, F.; Kilburn, P. Application of neural networks to estimate AADT on low-volume roads. J. Transp. Eng. 2001, 127, 426–432. [Google Scholar] [CrossRef]
- Balla, K.; Sevilla, R.; Hassan, O.; Morgan, K. An application of neural networks to the prediction of aerodynamic coefficients of aerofoils and wings. Appl. Math. Model. 2021, 96, 456–479. [Google Scholar] [CrossRef]
- Jia, Q.; Mwanandiye, E.S.; Tang, W.K.S. Master-slave synchronization of delayed neural networks with time-varying control. IEEE Trans. Neural Netw. Learn. Syst. 2021, 32, 2292–2298. [Google Scholar] [CrossRef]
- Wang, X.; Cao, J.D.; Wang, J.T.; Qi, J. A novel fixed-time stability strategy and its application to fixed-time synchronization control of semi-Markov jump delayed neural networks. Neurocomputing 2021, 452, 284–293. [Google Scholar] [CrossRef]
- Shi, C.Y.; Hoi, K.; Vong, S. Free-weighting-matrix inequality for exponential stability for neural networks with time-varying delay. Neurocomputing 2021, 466, 221–228. [Google Scholar] [CrossRef]
- Yang, B.; Hao, M.N.; Cao, J.J.; Zhao, X. Delay-dependent global exponential stability for neural networks with time-varying delay. Neurocomputing 2019, 338, 172–180. [Google Scholar] [CrossRef]
- Babcock, K.L.; Westervelt, R.M. Dynamics of simple electronic neural networks. Phys. D Nonlinear Phenom. 1987, 28, 305–316. [Google Scholar] [CrossRef]
- Angelaki, D.; Correia, M. Models of membrane resonance in pigeon semicircular canal type II hair cells. Biol. Cybern. 1991, 65, 1–10. [Google Scholar] [CrossRef]
- Wang, J.F.; Tian, L.X. Global Lagrange stability for inertial neural networks with mixed time-varying delays. Neurocomputing 2017, 235, 140–146. [Google Scholar] [CrossRef]
- Chen, D.D.; Kong, F.C. Delay-dependent criteria for global exponential stability of time-varying delayed fuzzy inertial neural networks. Neural Comput. Appl. 2021, 53, 49–68. [Google Scholar] [CrossRef]
- Shi, J.C.; Zeng, Z.G. Global exponential stabilization and lag synchronization control of inertial neural networks with time delays. Neural Netw. 2020, 126, 11–20. [Google Scholar] [CrossRef] [PubMed]
- Wang, Z.D.; Ho, D.W.C.; Liu, X.H. State estimation for delayed neural networks. IEEE Trans. Neural Netw. 2005, 16, 279–284. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Syed, A.M.; Saravanan, S.; Zhu, Q.X. Non-fragile finite-time H∞ state estimation of neural networks with distributed time-varying delay. J. Frankl. Inst. 2017, 354, 7566–7584. [Google Scholar] [CrossRef]
- Ren, J.; Liu, X.; Zhu, H.; Zhong, S.; Shi, K. State estimation of neural networks with two Markovian jumping parameters and multiple time delays. J. Frankl. Inst. 2017, 354, 812–833. [Google Scholar] [CrossRef]
- Tan, G.Q.; Wang, J.D.; Wang, Z.S. A new result on L2–L∞ performance state estimation of neural networks with time-varying delay: A new result on L2-L∞ performance state estimation of neural networks with time-varying delay. Neurocomputing 2020, 398, 166–171. [Google Scholar] [CrossRef]
- Tan, G.Q.; Wang, J.D.; Wang, Z.S. Extended dissipativity state estimation for generalized neural networks with time-varying delay via delay-product-type functionals and integral inequality. Neurocomputing 2021, 455, 78–87. [Google Scholar] [CrossRef]
- Sun, L.; Su, L.; Wang, J. Non-fragile dissipative state estimation for semi-Markov jump inertial neural networks with reaction-diffusion. Appl. Math. Comput. 2021, 411, 126404. [Google Scholar] [CrossRef]
- Wang, J.; Hu, X.H.; Cao, J.D.; Park, J.H.; Shen, H. H∞ state estimation for switched inertial neural networks with time-varying delays: A persistent dwell-time scheme. IEEE Trans. Neural Netw. Learn. Syst. 2021, 228, 1–11. [Google Scholar] [CrossRef]
- Gong, W.Q.; Liang, J.L.; Kan, X.; Nie, X. Robust state estimation for delayed complex-valued neural networks. Neural Process. Lett. 2017, 46, 1009–1029. [Google Scholar] [CrossRef]
- Zhang, Z.Q.; Zheng, T. Global asymptotic stability of periodic solutions for delayed complex-valued Cohen–Grossberg neural networks by combining coincidence degree theory with LMI method. Neurocomputing 2018, 289, 220–230. [Google Scholar] [CrossRef]
- Liang, J.; Li, K.L.; Song, Q.K.; Zhao, Z.; Liu, Y.; Alsaadi, F.E. State estimation of complex-valued neural networks with two additive time-varying delays. Neurocomputing 2018, 309, 54–61. [Google Scholar] [CrossRef]
- Gong, W.Q.; Liang, J.L.; Kan, X.; Wang, L.; Dobaie, A.M. Robust state estimation for stochastic complex-valued neural networks with sampled-data. Neural Comput. Appl. 2019, 31, 523–542. [Google Scholar] [CrossRef]
- Wan, P.; Jian, J.G. Global mittag-leffler boundedness for fractional-order complex-valued cohen-grossberg neural networks. Neural Process. Lett. 2019, 49, 121–139. [Google Scholar] [CrossRef]
- Wang, S.Z.; Zhang, Z.Y.; Lin, C.; Chen, J. Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control. Chaos Soliton. Fractals 2021, 153, 111583. [Google Scholar] [CrossRef]
- Gunasekaran, N.; Zhai, G.S. Sampled-data state-estimation of delayed complex-valued neural networks. Int. J. Syst. Sci 2020, 51, 303–312. [Google Scholar] [CrossRef]
- Hu, B.X.; Song, Q.K.; Zhao, Z.Q. Robust state estimation for fractional-order complex-valued delayed neural networks with interval parameter uncertainties: LMI approach. Appl. Math. Comput. 2020, 373, 1–12. [Google Scholar] [CrossRef]
- Aouiti, C.; Bessifi, M. Sliding mode control for finite-time and fixed-time synchronization of delayed complex-valued recurrent neural networks with discontinuous activation functions and nonidentical parameters. Eur. J. Control 2021, 59, 109–122. [Google Scholar] [CrossRef]
- Kumar, A.; Das, S.; Yadav, V.K. Global quasi-synchronization of complex-valued recurrent neural networks with time-varying delay and interaction terms. Chaos Soliton. Frac. 2021, 152, 111323. [Google Scholar] [CrossRef]
- Ding, Z.X.; Zhang, H.; Zeng, Z.; Yang, L.; Li, S. Global dissipativity and quasi-mittag-leffler synchronization of fractional-order discontinuous complex-valued neural networks. IEEE Trans. Neural Netw. Learn. Syst. 2021, 1–14. [Google Scholar] [CrossRef]
- Liu, X.; Yu, Y.G. Synchronization analysis for discrete fractional-order complex-valued neural networks with time delays. Neural Comput. Appl. 2021, 33, 10503–10514. [Google Scholar] [CrossRef]
- Zhang, Z.Y.; Guo, R.N.; Liu, X.P.; Zhong, M.; Lin, C.; Chen, B. Fixed-time synchronization for complex-valued BAM neural networks with time delays. Asian J. Control 2021, 23, 298–314. [Google Scholar] [CrossRef]
- Qiu, B.; Liao, X.F.; Zhou, B. State estimation for complex-valued neural networks with time-varying delays. In Proceedings of the Sixth International Conference on Intelligent Control and Information Processing (ICICIP), Wuhan, China, 26–28 November 2015; pp. 531–536. [Google Scholar]
- Guo, R.N.; Lu, J.W.; Li, Y.M.; Lv, W. Fixed-time synchronization of inertial complex-valued neural networks with time delays. Nonlinear Dyn. 2021, 105, 1643–1656. [Google Scholar] [CrossRef]
- Tang, Q.; Jian, J.G. Global exponential convergence for impulsive inertial complex-valued neural networks with time-varying delays. Math. Comput. Simul. 2019, 159, 39–56. [Google Scholar] [CrossRef]
- Li, X.F.; Huang, T.W. Adaptive synchronization for fuzzy inertial complex-valued neural networks with state-dependent coefficients and mixed delays. Fuzzy Sets Syst. 2021, 411, 174–189. [Google Scholar] [CrossRef]
- Yu, J.; Hu, C.; Jiang, H.J.; Wang, L. Exponential and adaptive synchronization of inertial complex-valued neural networks: A non-reduced order and non-separation approach. Neural Netw. 2021, 124, 50–59. [Google Scholar] [CrossRef]
- Yu, Y.N.; Zhang, Z.Y.; Zhong, M.Y.; Wang, Z. Pinning synchronization and adaptive synchronization of complex-valued inertial neural networks with time-varying delays in fixed-time interval. J. Frankl. Inst. 2022, 359, 1434–1456. [Google Scholar] [CrossRef]
- Guo, R.N.; Xu, S.Y.; Ma, Q.; Zhang, Z. Fixed-time synchronization of complex-valued inertial neural networks via nonreduced-order method. IEEE Syst. J. 2021, 1–9. [Google Scholar] [CrossRef]
- Long, C.Q.; Zhang, G.D.; Zeng, Z.G.; Hu, J. Finite-time stabilization of complex-valued neural networks with proportional delays and inertial terms: A non-separation approach. Neural Netw. 2022, 148, 86–95. [Google Scholar] [CrossRef]
- Du, F.F.; Lu, J.G. New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays. Chaos Soliton. Frac. 2021, 151, 111225. [Google Scholar] [CrossRef]
- Nagamani, G.; Rajan, G.S.; Zhu, Q.X. Exponential state estimation for memristor-based discrete-time BAM neural networks with additive delay components. IEEE Trans. Cybern. 2020, 50, 4281–4292. [Google Scholar] [CrossRef]
- Chen, X.F.; Song, Q.K. State estimation for quaternion-valued neural networks with multiple time delays. IEEE Trans. Syst. Man Cybern. Syst. 2019, 49, 2278–2287. [Google Scholar] [CrossRef]
- Liu, L.B.; Chen, X.F. State estimation of quaternion-valued neural networks with leakage time delay and mixed two additive time-varying delays. Neural Process. Lett. 2020, 51, 2155–2178. [Google Scholar] [CrossRef]
- Li, X.F.; Fang, J.A.; Huang, T.W. Event-triggered exponential stabilization for state-based switched inertial complex-valued neural networks with multiple delays. IEEE Trans. Cybern. 2020. [Google Scholar] [CrossRef] [PubMed]
- Wei, X.F.; Zhang, Z.Y.; Lin, C.; Chen, J. Synchronization and anti-synchronization for complex-valued inertial neural networks with time-varying delays. Appl. Math. Comput. 2021, 403, 126194. [Google Scholar] [CrossRef]
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Yu, Y.; Zhang, Z. State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays. Mathematics 2022, 10, 1725. https://doi.org/10.3390/math10101725
Yu Y, Zhang Z. State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays. Mathematics. 2022; 10(10):1725. https://doi.org/10.3390/math10101725
Chicago/Turabian StyleYu, Yaning, and Ziye Zhang. 2022. "State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays" Mathematics 10, no. 10: 1725. https://doi.org/10.3390/math10101725