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马跃,苏磊,张玉峰. 基于半马尔科夫的时滞神经网络输出反馈同步[J]. 安徽工业大学学报(自然科学版),xxxx,x(x):x-xx. doi: 10.12415/j.issn.1671-7872.24001
引用本文: 马跃,苏磊,张玉峰. 基于半马尔科夫的时滞神经网络输出反馈同步[J]. 安徽工业大学学报(自然科学版),xxxx,x(x):x-xx. doi: 10.12415/j.issn.1671-7872.24001
MA Yue, SU Lei, ZHANG Yufeng. Output Feedback Synchronization for Delayed Neural Networks Based on a Semi-Markov Approach[J]. Journal of Anhui University of Technology(Natural Science). DOI: 10.12415/j.issn.1671-7872.24001
Citation: MA Yue, SU Lei, ZHANG Yufeng. Output Feedback Synchronization for Delayed Neural Networks Based on a Semi-Markov Approach[J]. Journal of Anhui University of Technology(Natural Science). DOI: 10.12415/j.issn.1671-7872.24001

基于半马尔科夫的时滞神经网络输出反馈同步

Output Feedback Synchronization for Delayed Neural Networks Based on a Semi-Markov Approach

  • 摘要: 针对具有时变时滞的半马尔科夫神经网络静态输出反馈主从同步的问题,设计1种静态输出反馈控制器,以实现半马尔科夫神经网络从系统在时变时滞的影响下与主系统同步。利用半马尔科夫切换过程对时变时滞神经网络系统建模,表征神经网络系统参数的突变现象,比起马尔科夫过程,半马尔科夫过程更具一般性;考虑到系统状态不能完全获得的情况,利用输出信息实现神经网络之间的同步;利用李雅普诺夫(Lyapunov)稳定性理论,选取时滞相关的Lyapunov泛函并结合积分不等式缩放技术,得到低保守性的充分条件;在没有控制器输入矩阵的情况下,采用自由权矩阵技术将系统矩阵从Lyapunov泛函广义矩阵中分离,克服固定权矩阵的保守性;最后通过1个数值算例验证控制器设计的有效性。结果表明:设计的控制器可使时变时滞系统在初始状态与主系统不同步时,依然可在5 s后消除误差实现同步;控制信号在消除误差后趋向稳定,在保证同步误差系统随机均方稳定的同时满足混合无穷/无源性能指标,证明了设计的合理性。

     

    Abstract: To address the problem of static output feedback master-slave synchronization in semi Markov neural networks with time-varying delays, a static output feedback controller was designed to achieve synchronization between the semi Markov neural network slave system and the master system under the influence of time-varying delays. A semi-Markov switching process was used to model time-varying time-delay neural network systems, and to characterize the phenomenon of sudden changes in neural network system parameters. Compared to Markov processes, semi Markov processes were more general. Considering the situation where the system state couldn’t be fully obtained, the output information was used to achieve synchronization between neural networks. Using Lyapunov stability theory, selecting time-delay dependent Lyapunov functionals and combining them with integral inequality scaling techniques to obtain sufficient conditions for low conservatism. In the absence of a controller input matrix, the free weight matrix technique was used to separate the system matrix from the Lyapunov functional generalized matrix, overcoming the conservatism of a fixed weight matrix. Finally, the effectiveness of the controller design was verified through one numerical example. The results show that the designed controller can still eliminate errors and achieve synchronization in 5 s even when the initial state of the time-varying time-delay system is not synchronized with the main system. The control signal also tends to stabilize after eliminating errors, ensuring the random mean square stability of the synchronization error system while meeting the mixed infinite/passive performance indicators, proving the rationality of the design.

     

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