Saturated impulsive control for synchronization of coupled delayed neural networks. (English) Zbl 1526.93099
Summary: The paper focuses on the synchronization problem for a class of coupled neural networks with impulsive control, where the saturation structure of impulse action is fully considered. The coupled neural networks under consideration are subject to mixed delays including transmission delay and coupled delay. The sector condition in virtue of a new constraint of set inclusion is given for a addressed network, based on which a sufficient condition for exponential synchronization problem is obtained by replacing saturation nonlinearity with a dead-zone function. In the framework of saturated impulses, our results relying on the domain of attraction can still achieve the synchronization of coupled delayed neural networks. In addition, the estimating domain of attraction is proposed as large as possible by solving an optimization problem. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the proposed results.
MSC:
| 93C27 | Impulsive control/observation systems |
| 93D99 | Stability of control systems |
| 93B70 | Networked control |
| 93C43 | Delay control/observation systems |
Keywords:
impulse saturation; synchronization control; coupled neural networks; delay; domain of attraction; algorithmReferences:
| [1] | Ali, M. Syed; Usha, M.; Orman, Zeynep; Arik, Sabri, Improved result on state estimation for complex dynamical networks with time varying delays and stochastic sampling via sampled-data control, Neural Networks, 114, 28-37 (2019) · Zbl 1441.93306 |
| [2] | Berman, A.; Plemmons, R., Nonnegative Matrices in Mathematical Sciences (1979), New York: Academic · Zbl 0484.15016 |
| [3] | Cao, Yong-Yan; Lin, Zongli; Ward, David G., Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances, Automatica, 40, 7, 1221-1228 (2004) · Zbl 1056.93022 |
| [4] | Chen, Yonggang; Wang, Zidong; Shen, Bo; Dong, Hongli, Exponential synchronization for delayed dynamical networks via intermittent control: dealing with actuator saturations, IEEE Transactions on Neural Networks and Learning Systems, 30, 4, 1000-1012 (2018) |
| [5] | Da Silva, J. M. Gomes; Tarbouriech, Sophie, Antiwindup design with guaranteed regions of stability: an LMI-based approach, IEEE Transactions on Automatic Control, 50, 1, 106-111 (2005) · Zbl 1365.93443 |
| [6] | Duan, Lian; Huang, Lihong; Guo, Zhenyuan; Fang, Xianwen, Periodic attractor for reaction-diffusion high-order hopfield neural networks with time-varying delays, Computers & Mathematics with Applications, 73, 2, 233-245 (2017) · Zbl 1386.35159 |
| [7] | Guan, Zhi-Hong; Hill, David John; Shen, Xuemin, On hybrid impulsive and switching systems and application to nonlinear control, IEEE Transactions on Automatic Control, 50, 7, 1058-1062 (2005) · Zbl 1365.93347 |
| [8] | Guan, Zhi-Hong; Liu, Zhi-Wei; Feng, Gang; Wang, Yan-Wu, Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control, IEEE Transactions on Circuits and Systems. I. Regular Papers, 57, 8, 2182-2195 (2010) · Zbl 1468.93086 |
| [9] | He, Wangli; Qian, Feng; Cao, Jinde, Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control, Neural Networks, 85, 1-9 (2017) · Zbl 1429.93351 |
| [10] | Hespanha, Joao P., & Morse, A. Stephen (1999). Stability of switched systems with average dwell-time. In Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No. 99CH36304), Vol. 3 (pp. 2655-2660). |
| [11] | Hu, Tingshu; Lin, Zongli, Control systems with actuator saturation: analysis and design (2001), Springer Science & Business Media · Zbl 1061.93003 |
| [12] | Hu, Tingshu; Teel, Andrew R.; Zaccarian, Luca, Stability and performance for saturated systems via quadratic and nonquadratic Lyapunov functions, IEEE Transactions on Automatic Control, 51, 11, 1770-1786 (2006) · Zbl 1366.93439 |
| [13] | Kuntimad, G.; Ranganath, Heggere S., Perfect image segmentation using pulse coupled neural networks, IEEE Transactions on Neural Networks, 10, 3, 591-598 (1999) |
| [14] | Kwon, O. M.; Park, Ju H.; Lee, S. M., Secure communication based on chaotic synchronization via interval time-varying delay feedback control, Nonlinear Dynamics, 63, 1-2, 239-252 (2011) · Zbl 1215.93127 |
| [15] | Lee, Tae H.; Park, Ju H.; Lee, Sang-Moon; Kwon, O. M., Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control, International Journal of Control, 86, 1, 107-119 (2013) · Zbl 1278.93159 |
| [16] | Li, Hongfei; Li, Chuandong; Ouyang, Deqiang; Nguang, Sing Kiong, Impulsive synchronization of unbounded delayed inertial neural networks with actuator saturation and sampled-data control and its application to image encryption, IEEE Transactions on Neural Networks and Learning Systems, Early Access (2020) |
| [17] | Li, Yuanlong; Lin, Zongli, Improvements to the linear differential inclusion approach to stability analysis of linear systems with saturated linear feedback, Automatica, 49, 3, 821-828 (2013) · Zbl 1267.93143 |
| [18] | Li, Yuanlong; Lin, Zongli, Stability and performance of control systems with actuator saturation (2018), Springer · Zbl 1415.93005 |
| [19] | Li, Xiaodi; O’Regan, Donal; Akca, Haydar, Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays, IMA Journal of Applied Mathematics, 80, 1, 85-99 (2015) · Zbl 1316.34079 |
| [20] | Li, Xiaodi; Yang, Xueyan; Huang, Tingwen, Persistence of delayed cooperative models: Impulsive control method, Applied Mathematics and Computation, 342, 130-146 (2019) · Zbl 1428.34113 |
| [21] | Liu, Ziqian, Design of nonlinear optimal control for chaotic synchronization of coupled stochastic neural networks via Hamilton-Jacobi-bellman equation, Neural Networks, 99, 166-177 (2018) · Zbl 1441.93344 |
| [22] | Lu, Jianquan; Ho, Daniel W. C.; Cao, Jinde, A unified synchronization criterion for impulsive dynamical networks, Automatica, 46, 7, 1215-1221 (2010) · Zbl 1194.93090 |
| [23] | Lv, XiaoXiao; Li, Xiaodi; Cao, Jinde; Perc, Matjavz, Dynamical and static multisynchronization of coupled multistable neural networks via impulsive control, IEEE Transactions on Neural Networks and Learning Systems, 29, 12, 6062-6072 (2018) |
| [24] | Ouyang, Deqiang; Shao, Jie; Jiang, Haijun; Nguang, Sing Kiong; Shen, Heng Tao, Impulsive synchronization of coupled delayed neural networks with actuator saturation and its application to image encryption, Neural Networks, 128, 158-171 (2020) · Zbl 1471.93147 |
| [25] | Senan, Sibel; Ali, M. Syed; Vadivel, R.; Arik, Sabri, Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays, Neural Networks, 86, 32-41 (2017) · Zbl 1429.93010 |
| [26] | Song, Qiankun; Chen, Yanxi; Zhao, Zhenjiang; Liu, Yurong; Alsaadi, Fuad E., Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties, Neurocomputing, 420, 70-81 (2021) |
| [27] | Song, Qiankun; Long, Luyu; Zhao, Zhenjiang; Liu, Yurong; Alsaadi, Fuad E., Stability criteria of quaternion-valued neutral-type delayed neural networks, Neurocomputing, 412, 287-294 (2020) |
| [28] | Stamova, Ivanka; Stamov, Trayan; Li, Xiaodi, Global exponential stability of a class of impulsive cellular neural networks with supremums, International Journal of Adaptive Control and Signal Processing, 28, 11, 1227-1239 (2014) · Zbl 1338.93316 |
| [29] | Sun, Jitao; Qiao, Fei; Wu, Qidi, Impulsive control of a financial model, Physics Letters. A, 335, 4, 282-288 (2005) · Zbl 1123.91325 |
| [30] | Tan, Fei; Zhou, Lili; Chu, Yuming; Li, Yongmin, Fixed-time stochastic outer synchronization in double-layered multi-weighted coupling networks with adaptive chattering-free control, Neurocomputing, 399, 8-17 (2020) |
| [31] | Tarbouriech, Sophie; Garcia, Germain; da Silva, João Manoel Gomes; Queinnec, Isabelle, Stability and stabilization of linear systems with saturating actuators (2011), Springer Science & Business Media · Zbl 1279.93004 |
| [32] | Wei, Wu; Zhou, Wenjuan; Chen, Tianping, Cluster synchronization of linearly coupled complex networks under pinning control, IEEE Transactions on Circuits and Systems. I. Regular Papers, 56, 4, 829-839 (2008) · Zbl 1468.93140 |
| [33] | Xiong, Zhili; Zhang, Zhengle; Ma, Tiedong, Variable impulsive synchronization of memristor-based chaotic systems with actuator saturation, IEEE Access, 7, 185839-185848 (2019) |
| [34] | Yang, Tao; Chua, Leon O., Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication, IEEE Transactions on Circuits and Systems I, 44, 10, 976-988 (1997) |
| [35] | Yang, Xinsong; Li, Xiaodi; Lu, Jianquan; Cheng, Zunshui, Synchronization of time-delayed complex networks with switching topology via hybrid actuator fault and impulsive effects control, IEEE Transactions on Cybernetics, 50, 9, 4043-4052 (2020) |
| [36] | Yang, Xueyan; Li, Xiaodi; Xi, Qiang; Duan, Peiyong, Review of stability and stabilization for impulsive delayed systems, Mathematical Biosciences & Engineering, 15, 6, 1495 (2018) · Zbl 1416.93159 |
| [37] | Yu, Wenwu; Cao, Jinde; Lu, Jinhu, Global synchronization of linearly hybrid coupled networks with time-varying delay, SIAM Journal on Applied Dynamical Systems, 7, 1, 108-133 (2008) · Zbl 1161.94011 |
| [38] | Zaccarian, Luca; Teel, Andrew R., Modern anti-windup synthesis: control augmentation for actuator saturation, Vol. 36 (2011), Princeton University Press |
| [39] | Zhang, Yijun; Bao, Yuangui, Event-triggered hybrid impulsive control for synchronization of memristive neural networks, Science China. Information Sciences, 63, 1-12 (2020) |
| [40] | Zhang, Huaguang; Ma, Tiedong; Huang, Guang-Bin; Wang, Zhiliang, Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control, IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 40, 3, 831-844 (2009) |
| [41] | Zhu, Chenhong; Li, Xiaodi; Wang, Kening, An anti-windup approach for nonlinear impulsive system subject to actuator saturation, Chaos, Solitons & Fractals, 133, Article 109658 pp. (2020) · Zbl 1483.93245 |
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.
