[1]YUAN Xiaolin,MO Lipo.Adaptive H∞ synchronization of a class of fractional-order neural networks[J].CAAI Transactions on Intelligent Systems,2019,14(2):239-245.[doi:10.11992/tis.201709045]
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Adaptive H∞ synchronization of a class of fractional-order neural networks
CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume:
14
Number of periods:
2019 2
Page number:
239-245
Column:
学术论文—机器学习
Public date:
2019-03-05
- Title:
- Adaptive H∞ synchronization of a class of fractional-order neural networks
- Keywords:
- fractional-order; neural networks; adaptive; H∞; synchronization; unknown parameters; identification; controller
- CLC:
- TP18;O193
- DOI:
- 10.11992/tis.201709045
- Abstract:
- This study aims to address the adaptive H∞ synchronization problem and parameter identification problem of a class of uncertain fractional order neural networks. First, an adaptive control law is proposed to make the closed-loop system achieve H∞ synchronization. Second, by using the robust control method and Gronwall-Bellman inequality, it is shown that the drive system and the response system can achieve synchronization under the proposed control law while satisfying the H∞ performance. Finally, by numerical simulations, the effectiveness of the control law is verified, illustrating that the unknown parameters can also be identified using the proposed control law.
- References:
-
[1] ZHANG Shou, YU Yongguang, YU Junzhi. LMI conditions for global stability of fractional-order neural networks[J]. IEEE transactions on neural networks and learning systems, 2017, 28(10):2423-2433.
[2] LI Yan, CHEN Yangquan, PODLUBNY I. Mittag-Leffler stability of fractional order nonlinear dynamic systems[J]. Automatica, 2009, 45(8):1965-1969.
[3] HAYMAN S. The McCulloch-pitts model[C]//International Joint Conference on Neural Networks. Washington, USA, 1999:4438-4439.
[4] HOPFIELD J J. Neural networks and physical systems with emergent collective computational abilities[J]. Proceedings of the national academy of sciences of the United States of America, 1982, 79(8):2554-2558.
[5] YAN Zheng, WANG Jun. Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks[J]. IEEE transactions on neural networks and learning systems, 2014, 25(3):457-469.
[6] PAN Yunpeng, WANG Jun. Robust model predictive control using a discrete-time recurrent neural network[C]//International Symposium on Neural Networks:advances in Neural Networks. Berlin, Heidelberg, Germany:, 2008:883-892.
[7] KASLIK E, SIVASUNDARAM S. Multistability in impulsive hybrid Hopfield neural networks with distributed delays[J]. Nonlinear analysis:real world applications, 2011, 12(3):1640-1649.
[8] BAO Haibo, PARK J H, CAO Jinde. Adaptive synchronization of fractional-order memristor-based neural networks with time delay[J]. Nonlinear dynamics, 2015, 82(3):1343-1354.
[9] CHEN Jiejie, ZENG Zhigang, JIANG Ping. Global mittag-leffler stability and synchronization of memristor-based fractional-order neural networks[J]. Neural networks, 2014, 51:1-8.
[10] WU Wei, CHEN Tianping. Global synchronization criteria of linearly coupled neural network systems with time-varying coupling[J]. IEEE transactions on neural networks, 2008, 19(2):319-332.
[11] VELMURUGAN G, RAKKIYAPPAN R, CAO Jinde. Finite-time synchronization of fractional-order memristor-based neural networks with time delays[J]. Neural networks, 2016, 73:36-46.
[12] ABDURAHMAN A, JIANG Haijun, TENG Zhidong. Finite-time synchronization for memristor-based neural networks with time-varying delays[J]. Neural networks, 2015, 69:20-28.
[13] YU Juan, HU Cheng, JIANG Haijun. α-stability and α-synchronization for fractional-order neural networks[J]. Neural networks, 2012, 35:82-87.
[14] MA Weiyuan, LI Changpin, WU Yujiang, et al. Adaptive synchronization of fractional neural networks with unknown parameters and time delays[J]. Entropy, 2014, 16(12):6286-6299.
[15] LIN Peng, JIA Yingmin, LI Lin. Distributed robust H∞ consensus control in directed networks of agents with time-delay[J]. Systems and control letters, 2008, 57(8):643-653.
[16] MO L, JIA Y. H∞ consensus control of a class of high-order multi-agent systems[J]. IET control theory and application, 2011, 5(1):247-253.
[17] MATHIYALAGAN K, ANBUVITHYA R, SAKTHIVEL R, et al. Non-fragile H∞ synchronization of memristor-based neural networks using passivity theory[J]. Neural networks, 2016, 74:85-100.
[18] PODLUBNY I. Fractional differential equations:mathematics in science and engineering[M]. San Diego, Calif, USA:Academic Press, 1999.
[19] AGUILA-CAMACHO N, DUARTE-MERMOUD M A, GALLEGOS J A. Lyapunov functions for fractional order systems[J]. Communications in nonlinear science and numerical simulation, 2014, 19(9):2951-2957.
[20] KILBAS A A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Boston:Elsevier, 2006.
[21] SLOTINE J J E, LI Weiping. Applied nonlinear control[M]. Beijing, China Machine Press, 2004.
[22] TRIGEASSOU J C, MAAMRI N, SABATIER J, et al. A lyapunov approach to the stability of fractional differential equations[J]. Signal processing, 2011, 91(3):437-445.
[23] TRIGEASSOU J C, MAAMRI N. State space modeling of fractional differential equations and the initial condition problem[C]//Proceedings of the 6th International Multi-Conference on Systems, Signals and Devices. Djerba, Tunisia, 2009:1-7.
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Last Update:
2019-04-25