Finite-time synchronization of intermittently controlled reaction-diffusion systems with delays: a weighted LKF method. (English) Zbl 1527.35160
Summary: Considering the fact that existing methodologies for finite-time control are difficult to simultaneously overcome the difficulties induced by the effects of reaction-diffusion and time delay when intermittent control is confronted, this paper explores a novel Lyapunov-Krasovskii functional (LKF) method to investigate the finite-time synchronization of delayed reaction-diffusion systems. By designing a simple intermittent control and a weighted LKF, a general finite-time stability criterion is established first. Then, sufficient conditions for the finite-time synchronization of the interested system are given, where the weight factor of the LKF has a heavy influence on the settling time. Several important corollaries are also given to specify the usefulness and generality of the weighted LKF method and the finite-time stability criterion. Finally, a numerical example is provided to verify the new findings, and an image encryption algorithm is presented to validate the useful application of theoretical results.
MSC:
| 35K57 | Reaction-diffusion equations |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 93B52 | Feedback control |
Keywords:
finite-time synchronization; linear matrix inequalities; intermittent control; reaction-diffusion; time delay; master-slave synchronizationReferences:
| [1] | Lacitignola, D.; Bozzini, B.; Frittelli, M.; Sgura, I., Turing pattern formation on the sphere for a morphochemical reaction-diffusion model for electrodeposition. Commun Nonlinear Sci Numer Simul, 484-508 (2017) · Zbl 1510.92034 |
| [2] | Maslovskaya, A.; Moroz, L.; Chebotarev, A. Y.; Kovtanyuk, A. E., Theoretical and numerical analysis of the landau-khalatnikov model of ferroelectric hysteresis. Commun Nonlinear Sci Numer Simul (2021) · Zbl 1457.82448 |
| [3] | Chen, W. H.; Luo, S.; Zheng, W. X., Impulsive synchronization of reaction-diffusion neural networks with mixed delays and its application to image encryption. IEEE Trans Neural Netw Learn Syst, 12, 2696-2710 (2016) |
| [4] | Shanmugam, L.; Mani, P.; Rajan, R.; Joo, Y. H., Adaptive synchronization of reaction-diffusion neural networks and its application to secure communication. IEEE Trans Cybern, 3, 911-922 (2018) |
| [5] | Wang, L.; He, B.; Zeng, Z., Global synchronization of fuzzy memristive neural networks with discrete and distributed delays. IEEE Trans Fuzzy Syst, 9, 2022-2034 (2020) |
| [6] | Hu, C.; Yu, J.; Jiang, H.; Teng, Z., Exponential synchronization for reaction-diffusion networks with mixed delays in terms of p-norm via intermittent driving. Neural Netw, 1-11 (2012) · Zbl 1245.93122 |
| [7] | Chen, W. H.; Liu, L.; Lu, X., Intermittent synchronization of reaction-diffusion neural networks with mixed delays via razumikhin technique. Nonlinear Dynam, 1, 535-551 (2017) · Zbl 1371.34071 |
| [8] | Wu, T.; Xiong, L.; Cao, J.; Park, J. H.; Cheng, J., Synchronization of coupled reaction-diffusion stochastic neural networks with time-varying delay via delay-dependent impulsive pinning control algorithm. Commun Nonlinear Sci Numer Simul (2021) · Zbl 1467.93160 |
| [9] | Yang, X.; Song, Q.; Cao, J.; Lu, J., Synchronization of coupled Markovian reaction-diffusion neural networks with proportional delays via quantized control. IEEE Trans Neural Netw Learn Syst, 3, 951-958 (2018) |
| [10] | Lhachemi, H.; Shorten, R., Boundary feedback stabilization of a reaction-diffusion equation with robin boundary conditions and state-delay. Automatica (2020) · Zbl 1440.93202 |
| [11] | Lhachemi, H.; Malik, A.; Shorten, R., Integral action for setpoint regulation control of a reaction-diffusion equation in the presence of a state delay. Automatica (2021) · Zbl 1478.93204 |
| [12] | Wang, L.; Zhang, C., Exponential synchronization of memristor-based competitive neural networks with reaction-diffusions and infinite distributed delays. IEEE Trans Neural Netw Learn Syst (2022) |
| [13] | Haimo, V. T., Finite time controllers. SIAM J Control Optim, 4, 760-770 (1986) · Zbl 0603.93005 |
| [14] | Wang, J. L.; Zhang, X. X.; Wu, H. N.; Huang, T.; Wang, Q., Finite-time passivity and synchronization of coupled reaction-diffusion neural networks with multiple weights. IEEE Trans Cybern, 9, 3385-3397 (2018) |
| [15] | Liu, X.; Wei, Y., Finite-time synchronization under aperiodically intermittent control and its application on spatially coupled reaction-diffusion neural networks, 1-7 |
| [16] | Qiu, Q.; Su, H., Finite-time output synchronization of multiple weighted reaction-diffusion neural networks with adaptive output couplings. IEEE Trans Neural Netw Learn Syst (2022) |
| [17] | Wang, S.; Guo, Z.; Wen, S.; Huang, T.; Gong, S., Finite/fixed-time synchronization of delayed memristive reaction-diffusion neural networks. Neurocomputing, 1-8 (2020) |
| [18] | Duan, L.; Wang, Q.; Wei, H.; Wang, Z., Multi-type synchronization dynamics of delayed reaction-diffusion recurrent neural networks with discontinuous activations. Neurocomputing, 182-192 (2020) |
| [19] | Wei, R.; Cao, J.; Kurths, J., Fixed-time output synchronization of coupled reaction-diffusion neural networks with delayed output couplings. IEEE Trans Netw Sci Eng, 1, 780-789 (2021) |
| [20] | Duan, L.; Shi, M.; Huang, L., New results on finite-/fixed-time synchronization of delayed diffusive fuzzy HNNs with discontinuous activations. Fuzzy Sets and Systems, 141-151 (2021) · Zbl 1467.93014 |
| [21] | Moulay, E.; Dambrine, M.; Yeganefar, N.; Perruquetti, W., Finite-time stability and stabilization of time-delay systems. Systems Control Lett, 7, 561-566 (2008) · Zbl 1140.93447 |
| [22] | Efimov, D.; Polyakov, A.; Fridman, E.; Perruquetti, W.; Richard, J. P., Comments on finite-time stability of time-delay systems. Automatica, 7, 1944-1947 (2014) · Zbl 1296.93150 |
| [23] | Wang, Q.; Duan, L.; Wei, H.; Wang, L., Finite-time anti-synchronisation of delayed hopfield neural networks with discontinuous activations. Internat J Control, 9, 2398-2405 (2022) · Zbl 1500.93121 |
| [24] | Yang, X., Can neural networks with arbitrary delays be finite-timely synchronized?. Neurocomputing, 275-281 (2014) |
| [25] | Tang, R.; Yang, X.; Wan, X.; Zou, Y.; Cheng, Z.; Fardoun, H. M., Finite-time synchronization of nonidentical BAM discontinuous fuzzy neural networks with delays and impulsive effects via non-chattering quantized control. Commun Nonlinear Sci Numer Simul (2019) · Zbl 1476.93143 |
| [26] | Yang, X.; Song, Q.; Liang, J.; He, B., Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations. J Franklin Inst B, 10, 4382-4406 (2015) · Zbl 1395.93354 |
| [27] | Wang, Q.; Fu, B.; Lin, C.; Li, P., Exponential synchronization of chaotic lur’e systems with time-triggered intermittent control. Commun Nonlinear Sci Numer Simul (2022) · Zbl 1536.93734 |
| [28] | Hu, X.; Wang, L.; Zhang, C.; Wan, X.; He, Y., Fixed-time stabilization of discontinuous spatiotemporal neural networks with time-varying coefficients via aperiodically switching control. Sci China Inf Sci, 5 (2023) |
| [29] | Duan, L.; Wei, H.; Huang, L., Finite-time synchronization of delayed fuzzy cellular neural networks with discontinuous activations. Fuzzy Sets and Systems, 56-70 (2019) · Zbl 1423.93190 |
| [30] | Mei, J.; Jiang, M.; Xu, W.; Wang, B., Finite-time synchronization control of complex dynamical networks with time delay. Commun Nonlinear Sci Numer Simul, 9, 2462-2478 (2013) · Zbl 1311.34157 |
| [31] | Li, L.; Tu, Z.; Mei, J.; Jian, J., Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods. Nonlinear Dynam, 1, 375-388 (2016) · Zbl 1349.93167 |
| [32] | Yang, F.; Mei, J.; Wu, Z., Finite-time synchronisation of neural networks with discrete and distributed delays via periodically intermittent memory feedback control. IET Control Theory Appl, 14, 1630-1640 (2016) |
| [33] | Liu, M.; Jiang, H.; Hu, C., Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control. J Franklin Inst B, 13, 5374-5397 (2017) · Zbl 1395.93348 |
| [34] | Xu, C.; Yang, X.; Lu, J.; Feng, J.; Alsaadi, F. E.; Hayat, T., Finite-time synchronization of networks via quantized intermittent pinning control. IEEE Trans Cybern, 10, 3021-3027 (2018) |
| [35] | Zhang, D.; Shen, Y.; Mei, J., Finite-time synchronization of multi-layer nonlinear coupled complex networks via intermittent feedback control. Neurocomputing, 15, 129-138 (2017) |
| [36] | Zhou, Y.; Wan, X.; Huang, C.; Yang, X., Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control. Appl Math Comput (2020) · Zbl 1475.93115 |
| [37] | Chen, S.; Song, G.; Zheng, B. C.; Li, T., Finite-time synchronization of coupled reaction-diffusion neural systems via intermittent control. Automatica (2019) · Zbl 1429.92010 |
| [38] | Tang, R.; Su, H.; Zou, Y.; Yang, X., Finite-time synchronization of markovian coupled neural networks with delays via intermittent quantized control: Linear programming approach. IEEE Trans Neural Netw Learn Syst, 10, 5268-5278 (2022) |
| [39] | Liu, Y.; Wang, Z.; Yuan, Y.; Liu, W., Event-triggered partial-nodes-based state estimation for delayed complex networks with bounded distributed delays. IEEE Trans Syst Man Cybern: Syst, 6, 1088-1098 (2017) |
| [40] | Kammler, D. W., A first course in fourier analysis (2000), Cambridge University Press |
| [41] | Lu, J.; Cao, J.; Ho, D. W., Adaptive stabilization and synchronization for chaotic lur’e systems with time-varying delay. IEEE Trans Circuits Syst I Regul Pap, 5, 1347-1356 (2008) |
| [42] | Stallings, W.; Tahiliani, M. P., Cryptography and network security: principles and practice, Vol. 6 (2014), Pearson: Pearson London |
| [43] | Tan, X.; Xiang, C.; Cao, J.; Xu, W.; Wen, G.; Rutkowski, L., Synchronization of neural networks via periodic self-triggered impulsive control and its application in image encryption. IEEE Trans Cybern, 8, 8246-8257 (2021) |
| [44] | Tang, R.; Yang, X., Finite-time synchronization of complex networks with intermittent event-triggered control, 1-6 |
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.
