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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