Projective Synchronization of Fractional Quaternion Neural Networks With Time-Varying Delays
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摘要: 研究了具有时变时滞的分数阶四元数神经网络的投影同步问题. 该文不将分数阶四元数神经网络系统转化成两个复值系统或四个实值系统, 而是将四元数系统当做一个整体进行处理. 在合适的控制器下, 通过构造合适的Lyapunov函数, 并利用一些不等式技巧, 得到了具有时变时滞分数阶四元数时滞神经网络投影同步的充分性判据. 最后，通过数值仿真实例验证了所得结论的有效性和可行性.
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关键词:
- 分数阶四元数神经网络 /
- 时变时滞 /
- 投影同步 /
- 线性矩阵不等式
Abstract: The projective synchronization of fractional quaternion neural networks with time-varying delays was studied. Instead of transforming the fractional quaternion neural network system into 2 complex-valued systems or 4 real-valued systems, the means of treating the quaternion network system directly as a whole was applied. Under a rational controller, through the construction of a suitable Lyapunov function and with some inequality techniques, the sufficient criteria for the projective synchronization of fractional quaternion neural networks with time-varying delays were obtained. The numerical simulation example shows the validity and feasibility of the conclusions. -
图 1 未加控制时, 状态变量p1R，p2R，p1I，p2I，q1R，q2R，q1I，q2I的时间响应曲线
Figure 1. The time response curves of state variables p1R, p2R, p1I, p2I, q1R, q2R, q1I, q2I without control
图 2 未加控制时, 状态变量p1J，pJ2，p1K，p2K，q1J，q2J，q1K，q2K的时间响应曲线
Figure 2. The time response curves of state variables p1J, p2J, p1K, p2K, q1J, q2J, q1K, q2K without control
图 3 未加控制时, 误差变量θ1R(t)，θ2R(t)，θ1I(t)，θ2I(t)，θ1J(t)，θ2J(t)，θ1K(t)，θ2K(t)的时间响应曲线
Figure 3. Time response curves of error variables θ1R(t), θ2R(t), θ1I(t), θ2I(t), θ1J(t), θ2J(t), θ1K(t), θ2K(t) without control
图 4 投影矩阵为F=diag(1, 1), 施加控制时, 状态变量p1R，p2R，p1I，p2I，q1R, q2R，q1I，q2I的时间响应曲线
Figure 4. Projection matrix F=diag(1, 1), and the time response curves of state variables p1R, p2R, p1I, p2I, q1R, q2R, q1I, q2I with control
图 5 投影矩阵为F=diag(1, 1), 施加控制时, 状态变量p1J，p2J，p1K，p2K, q1J，q2J，q1K，q2K的时间响应曲线
Figure 5. Projection matrix F=diag(1, 1), and the time response curves of state variables p1J, p2J, p1K, p2K, q1J, q2J, q1K, q2K with control
图 6 投影矩阵为F=diag(1, 1), 施加控制时, 误差变量θ1R(t)，θ2R(t)，θ1I(t), θ2I(t)，θ1J(t)，θ2J(t)，θ1K(t)，θ2K(t)的时间响应曲线
Figure 6. Projection matrix F=diag(1, 1), and the time response curves of error variables θ1R(t), θ2R(t), θ1I(t), θ2I(t), θ1J(t), θ2J(t), θ1K(t), θ2K(t) with control
图 7 投影矩阵为F=diag(-1, -1), 施加控制时, 状态变量p1R，p2R，p1I，p2I, q1R，q2R，q1I，q2I的时间响应曲线
Figure 7. Projection matrix F=diag(-1, -1), and the time response curves of state variables p1R, p2R, p1I, p2I, q1R, q2R, q1I, q2I with control
图 8 投影矩阵为F=diag(-1, -1), 施加控制时, 状态变量p1J，p2J，p1K，p2K, q1J，q2J，q1K，q2K的时间响应曲线
Figure 8. Projection matrix F=diag(-1, -1), and the time response curves of state variables p1J, p2J, p1K, p2K, q1J, q2J, q1K, q2K with control
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[1] HOPPENSTEADT F C, IZHIKEVICH E M. Pattern recognition via synchronization in phase-locked loop neural networks[J]. IEEE Transactions on Neural Networks, 2000, 11: 734-738. doi: 10.1109/72.846744 [2] ALIMI A M, AOUITI C, ASSALI E A. Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication[J]. Neurocomputing, 2019, 332: 29-43. doi: 10.1016/j.neucom.2018.11.020 [3] SUBRAMANIAN K, MUTHUKUMAR P. Global asymptotic stability of complex-valued neural networks with additive time-varying delays[J]. Cognitive Neurodynamics, 2017, 11: 293-306. doi: 10.1007/s11571-017-9429-1 [4] 陈宇, 周博, 宋乾坤. 具有不确定性的分数阶时滞复值神经网络无源性[J]. 应用数学和力学, 2021, 42(5): 492-499. doi: 10.21656/1000-0887.410309CHEN Yu, ZHOU Bo, SONG Qiankun. Passivity of fractional-order delayed complex-valued neural networks with uncertainties[J]. Applied Mathematics Mechanics, 2021, 42(5): 492-499. (in Chinese) doi: 10.21656/1000-0887.410309 [5] 杜雨薇, 李兵, 宋乾坤. 事件触发下混合时滞神经网络的状态估计[J]. 应用数学和力学, 2020, 41(8): 887-898. doi: 10.21656/1000-0887.400377DU Yuwei, LI Bing, SONG Qiankun. Event-based state estimation for neural network with time-varying delay and infinite-distributed delay[J]. Applied Mathematics and Mechanics, 2020, 41(8): 887-898. (in Chinese) doi: 10.21656/1000-0887.400377 [6] YANG X J, SONG Q K, LIU Y R, et al. Finite-time stability analysis of fractional-order neural networks with delay[J]. Neurocomputing, 2015, 152: 19-26. doi: 10.1016/j.neucom.2014.11.023 [7] WANG X, PARK J H, YANG H L, et al. Delay-dependent fuzzy sampled-data synchronization of T-S fuzzy complex networks with multiple couplings[J]. IEEE Transactions on Fuzzy Systems, 2019, 28: 178-189. [8] TANG Z, PARK J H, WANG Y, et al. Distributed impulsive quasi-synchronization of Lure networks with proportional delay[J]. IEEE Transactions on Cybernetics, 2018, 49: 3105-3115. [9] CHEN J J, ZENG Z G, JIANG P. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks[J]. Neural Networks, 2014, 51: 1-8. doi: 10.1016/j.neunet.2013.11.016 [10] LI H L, HU C, CAO J, et al. Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays[J]. Neural Networks, 2019, 118: 102-109. doi: 10.1016/j.neunet.2019.06.008 [11] GU Y J, YU Y G, WANG H. Projective synchronization for fractional-order memristor-based neural networks with time delays[J]. Neural Computing and Applications, 2019, 31: 6039-6054. doi: 10.1007/s00521-018-3391-7 [12] GU Y J, YU Y G, WANG H. Synchronization-based parameter estimation of fractional-order neural networks[J]. Physica A: Statistical Mechanics and Its Applications, 2017, 483: 351-361. doi: 10.1016/j.physa.2017.04.124 [13] 张平奎, 杨绪君. 基于激励滑模控制的分数阶神经网络的修正投影同步研究[J]. 应用数学和力学, 2018, 39(3): 343-354. doi: 10.21656/1000-0887.380098ZHANG Pingkui, YANG Xujun. Modified projective synchronization of a class of fractional-order neural networks based on active sliding mode controll[J]. Applied Mathematics Mechanics, 2018, 39(3): 343-354. (in chinese) doi: 10.21656/1000-0887.380098 [14] YANG S, YU J, HU C, et al. Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks[J]. Neural Networks, 2018, 104: 104-113. doi: 10.1016/j.neunet.2018.04.007 [15] DING D W, YAO X L, ZHANG H W. Complex projection synchronization of fractional-order complex-valued memristive neural networks with multiple delays[J]. Neural Processing Letters, 2020, 51: 325-345. doi: 10.1007/s11063-019-10093-x [16] ZHANG L Z, YANG Y Q, WANG F. Synchronization analysis of fractional-order neural networks with time-varying delays via discontinuous neuron activations[J]. Neurocomputing, 2018, 275: 40-49. doi: 10.1016/j.neucom.2017.04.056 [17] LIU Y, ZHANG D, LOU J, et al. Stability analysis of quaternion-valued neural networks: decomposition and direct approaches[J]. IEEE Transactions on Neural Networks and Learning Systems, 2017, 29: 4201-4211. [18] SONG Q K, CHEN Y X, ZHAO Z J, et al. Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties[J]. Neurocomputing, 2021, 420: 70-81. doi: 10.1016/j.neucom.2020.08.059 [19] ZOU C M, KOU K I, WANG Y. Quaternion collaborative and sparse representation with application to color face recognition[J]. IEEE Transactions on Image Processing, 2016, 25: 3287-3302. doi: 10.1109/TIP.2016.2567077 [20] XIA Y L, JAHANCHAHI C, MANDIC D P. Quaternion-valued echo state networks[J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 26: 663-673. [21] MATSUI N, ISOKAWA T, KUSAMICHI H, et al. Quaternion neural network with geometrical operators[J]. Journal of Intelligent Fuzzy Systems, 2004, 15: 149-164. [22] KUMAR U, DAS S, HUANG C, et al. Fixed-time synchronization of quaternion-valued neural networks with time-varying delay[J]. Proceedings of the Royal Society A, 2020, 476: 20200324. doi: 10.1098/rspa.2020.0324 [23] XIAO J Y, ZHONG S M. Synchronization and stability of delayed fractional-order memristive quaternion-valued neural networks with parameter uncertainties[J]. Neurocomputing, 2019, 363: 321-338. doi: 10.1016/j.neucom.2019.06.044 [24] PAHNEHKOLAEI S M A, ALFI A, MACHADO J A T. Delay-dependent stability analysis of the QUAD vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks[J]. Neural Networks, 2019, 117: 307-327. doi: 10.1016/j.neunet.2019.05.015 [25] CHEN, X F, LI Z S, SONG Q K, et al. Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties[J]. Neural Networks, 2017, 91: 55-65. doi: 10.1016/j.neunet.2017.04.006 [26] LIN D Y, CHEN X F, LI B, et al. LMI conditions for some dynamical behaviors of fractional-order quaternion-valued neural networks[J]. Advances in Difference Equations, 2019, 2019(1): 226. doi: 10.1186/s13662-019-2163-8 -
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