Synchronization of fractional-order delayed coupled networks with reaction-diffusion terms and Neumann boundary value conditions. (English) Zbl 1532.93203
Summary: This paper investigates the adaptive pinning strategies for achieving synchronization of fractional-order delayed coupled networks with reaction-diffusion terms and a digraph topology by incorporating Neumann boundary value conditions. By employing the inf-sup method, a novel fractional-order inequality is proved. The classical Poincaré inequality is also extended by utilizing the Hölder inequality. Two types of control laws are developed to achieve synchronization: one with control gains dependent solely on time, and another with control gains dependent on both space and time. For each case, adaptive control laws and synchronization criteria based on matrix inequalities are proposed. Finally, the effectiveness of the synchronization results is demonstrated through two numerical examples.
MSC:
| 93C40 | Adaptive control/observation systems |
| 93D99 | Stability of control systems |
| 93B70 | Networked control |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35R11 | Fractional partial differential equations |
Keywords:
fractional-order coupled network; reaction-diffusion terms; synchronization; adaptive pinning controlReferences:
| [1] | Bao, H.; Park, J. H.; Cao, J., Adaptive synchronization of fractional-order output-coupling neural networks via quantized output control. IEEE Trans Neural Netw Learn Syst, 3230-3239 (2021) |
| [2] | Liu, P.; Zeng, Z.; Wang, J., Global synchronization of coupled fractional-order recurrent neural networks. IEEE Trans Neural Netw Learn Syst, 2358-2368 (2019) |
| [3] | Liu, C.; Wang, J.; Wu, H., Finite-time passivity for coupled fractional-order neural networks with multistate or multiderivative couplings. IEEE Trans Neural Netw Learn Syst (2021) |
| [4] | Strogatz, S., Exploring complex networks. Nature, 268-276 (2001) · Zbl 1370.90052 |
| [5] | He, X.; Ho, D.; Huang, T.; Yu, J.; Abu-Rub, H.; Li, C., Second-order continuous-time algorithms for economic power dispatch in smart grids. IEEE Trans Syst Man Cybern Syst, 1482-1492 (2018) |
| [6] | Ding, S.; Wang, Z., Synchronization of coupled neural networks via an event-dependent intermittent pinning control. IEEE Trans Syst Man Cybern Syst, 1928-1934 (2022) |
| [7] | Yu, W.; DeLellis, P.; Chen, G.; Bernardo, M.; Kurths, J., Distributed adaptive control of synchronization in complex networks. IEEE Trans Automat Control, 2153-2158 (2012) · Zbl 1369.93321 |
| [8] | Liu, P.; Li, Y.; Sun, J.; Wang, Y., Output synchronization analysis of coupled fractional-order neural networks with fixed and adaptive couplings. Neural Comput Appl, 517-528 (2022) |
| [9] | Wang, Q.; Wang, J., Finite-time output synchronization of undirected and directed coupled neural networks with output coupling. IEEE Trans Neural Netw Learn Syst, 2117-2128 (2021) |
| [10] | Wang, J.; Wang, Q.; Wu, H.; Huang, T., Finite-time output synchronization and \(H_\infty\) output synchronization of coupled neural networks with multiple output couplings. IEEE Trans Cybern, 6041-6053 (2022) |
| [11] | Zhang, X.; Li, C.; He, Z., Cluster synchronization of delayed coupled neural networks: Delay-dependent distributed impulsive control. Neural Netw, 34-43 (2021) · Zbl 1526.93254 |
| [12] | Jia, J.; Zeng, Z.; Wang, F., Pinning synchronization of fractional-order memristor-based neural networks with multiple time-varying delays via static or dynamic coupling. J Franklin Inst, 895-933 (2021) · Zbl 1455.93157 |
| [13] | Zhou S. Lin, W., Eliminating synchronization of coupled neurons adaptively by using feedback coupling with heterogeneous delays. Chaos (2021) · Zbl 1458.92019 |
| [14] | Ji, X.; Lu, J.; Jiang, B.; Shi, K., Distributed synchronization of delayed neural networks: delay-dependent hybrid impulsive control. IEEE Trans Netw Sci Eng, 634-647 (2022) |
| [15] | Yang, C.; Yang, Y.; Yang, C.; Zhu, J.; Zhang, A.; Qiu, J., Adaptive control for synchronization of semi-linear complex spatio-temporal networks with time-invariant coupling delay and time-variant coupling delay. Internat J Adapt Control Signal Process, 2640-2659 (2022) · Zbl 07842362 |
| [16] | Gong, S.; Guo, Z.; Wen, S.; Huang, T., Finite-time and fixed-time synchronization of coupled memristive neural networks with time delay. IEEE Trans Cybern, 2944-2955 (2021) |
| [17] | Diethelm, K., The analysis of fractional differential equations (2010), Springer · Zbl 1215.34001 |
| [18] | Kilbas, A.; Srivastava, H.; Trujillo, J., Theory and applications of fractional differential equations (2006), Elsevier: Elsevier Amsterdam · Zbl 1092.45003 |
| [19] | Wang, F.; Wang, F.; Liu, X., Further results on Mittag-Leffler synchronization of fractional-order coupled neural networks. Adv Differ Equ, 240 (2021) · Zbl 1494.34064 |
| [20] | Zheng, B.; Wang, Z., Adaptive synchronization of fractional-order complex-valued coupled neural networks via direct error method. Neurocomputing, 114-122 (2022) |
| [21] | Fan, H.; Zhu, J.; Wen, H., Comparison principle and synchronization analysis of fractional-order complex networks with parameter uncertainties and multiple time delays. AIMS Math, 12981-12999 (2022) |
| [22] | Zheng, B.; Wang, Z., Mittag-Leffler synchronization of fractional-order coupled neural networks with mixed delays. Appl Math Comput (2022) · Zbl 1510.34028 |
| [23] | Li, R.; Wu, H.; Cao, J., Impulsive exponential synchronization of fractional-order complex dynamical networks with derivative couplings via feedback control based on discrete time state observations. Acta Math Sci, 737-754 (2022) · Zbl 1513.93041 |
| [24] | Lu, J., Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Chaos Solitons Fractals, 116-125 (2008) · Zbl 1134.35066 |
| [25] | Chua, L.; Yang, L., Cellular neural networks: Theory. IEEE Trans Circuits Syst, 1257-1272 (1988) · Zbl 0663.94022 |
| [26] | Wang F, Wang H, Xu K. Diffusive logistic model towards predicting information diffusion in online social networks. In: Proc 32nd int conf distrib comput syst workshops. 2012, p. 133-9. |
| [27] | Wang, J.; Wu, H.; Huang, T.; Ren, S., Pinning control strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms. IEEE Trans Neural Netw Learn Syst, 749-761 (2016) |
| [28] | Wei, R.; Cao, J.; Kurths, J., Fixed-time output synchronization of coupled reaction-diffusion neural networks with delayed output coupling. IEEE Trans Netw Sci Eng, 780-789 (2021) |
| [29] | Wang, J.; Wu, H.; Huang, T.; Ren, S., Passivity and synchronization of linearly coupled reaction-diffusion neural networks with adaptive coupling. IEEE Trans Cybern (2015), 1942-1952 |
| [30] | Wang, J.; Wu, H., Synchronization and adaptive control of an array of linearly coupled reaction-diffusion neural networks with hybrid coupling. IEEE Trans Cybern, 1350-1361 (2014) |
| [31] | Wu, T.; Xiong, L.; Cao, J.; Park, J.; Cheng, J., Synchronization of coupled reaction-diffusion stochastic neural networks with time-varying delay via delay-dependent impulsive pinning control algorithm. Commun Nonlinear Sci (2021) · Zbl 1467.93160 |
| [32] | Benson, D.; Wheatcraft, S. W.; Meerschaert, M., Application of a fractional advection-dispersion equation. Water Resour Res, 1403-1412 (2000) |
| [33] | del Castillo-Negrete, D.; Carreras, B.; Lynch, V. E., Non-diffusive transport in plasma turbulence: A fractional diffusion approach. Phys Rev Lett (2005) |
| [34] | Narayanan, G.; Ali, M.; Alsulami, H.; Ahmad, B.; Trujillo, J., A hybrid impulsive and sampled-data control for fractional-order delayed reaction-diffusion system of mRNA and protein in regulatory mechanisms. Commun Nonlinear Sci (2022) · Zbl 1490.92027 |
| [35] | Yan, X.; Yang, C.; Cao, J.; Korovin, I.; Gorbachev, S.; Gorbacheva, N., Boundary consensus control strategies for fractional-order multi-agent systems with reaction-diffusion terms. Inform Sci, 461-473 (2022) · Zbl 1536.93827 |
| [36] | Sun, Q.; Xiao, M.; Tao, B., Local bifurcation analysis of a fractional-order dynamic model of genetic regulatory networks with delays. Neural Process Lett, 1285-1296 (2018) |
| [37] | Stamova, I.; Stamov, G., Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers. Neural Netw, 22-32 (2017) · Zbl 1441.93106 |
| [38] | Li, W.; Gao, X.; Li, R., Dissipativity and synchronization control of fractional-order memristive neural networks with reaction-diffusion terms. Math Method Appl Sci, 7494-7505 (2019) · Zbl 1434.35265 |
| [39] | Chen, W.; Yu, Y.; Hai, X.; Ren, G., Adaptive quasi-synchronization control of heterogeneous fractional-order coupled neural networks with reaction-diffusion. Appl Math Comput (2022) · Zbl 1510.93120 |
| [40] | Lv, Y.; Hu, C.; Yu, J.; Jiang, H.; Huang, T., Edge-based fractional-order adaptive strategies for synchronization of fractional-order coupled networks with reaction-diffusion terms. IEEE Trans Cybern, 1582-1594 (2020) |
| [41] | Wang, F.; Yang, Y.; Hu, M.; Xu, X., Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control. Physica A, 134-143 (2015) · Zbl 1400.93149 |
| [42] | Ouannas, A.; Wang, X.; Pham, V.; Grassi, G.; Huynh, V., Synchronization results for a class of fractional-order spatiotemporal partial differential systems based on fractional Lyapunov approach. Boun Value Probl (2019) · Zbl 1503.35271 |
| [43] | Cai, R.; Kou, C., Mittag-Leffler stabilization for coupled fractional reaction-diffusion neural networks subject to boundary matched disturbance. Math Method Appl Sci, 3143-3156 (2023) · Zbl 1530.35034 |
| [44] | Wang, F.; Liu, X.; Li, J., Synchronization analysis for fractional non-autonomous neural networks by a Halanay inequality. Neurocomputing, 20-29 (2018) |
| [45] | Kassim, M.; Tatar, N., Nonlinear fractional distributed Halanay inequality and application to neural network systems. Chaos Solitons Fractals (2021) · Zbl 1498.34150 |
| [46] | He, B.; Zhou, H.; Chen, Y.; Kou, C., Asymptotical stability of fractional order systems with time delay via an integral inequality. IET Control Theory A, 1748-1754 (2018) |
| [47] | Lu, J., Robust global exponential stability for interval reaction-diffusion hopfield neural networks with distributed delays. IEEE Trans Circuits Syst II, 1115-1119 (2007) |
| [48] | Hu, C.; Jiang, H.; Teng, Z., Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms. IEEE Trans Neural Netw, 67-81 (2010) |
| [49] | Li, Y.; Chen, Y.; Podlubny, I., Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica, 1965-1969 (2009) · Zbl 1185.93062 |
| [50] | Song, X.; Li, X.; Song, S.; Ahn, C. K., State observer design of coupled genetic regulatory networks with reaction-diffusion terms via time-space sampled-data communications. IEEE/ACM Trans Comput Biol Bioinform, 3704-3714 (2022) |
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