切换递归神经网络的稳定性分析和设计问题研究

The switched recurrent neural networks has the characterics both switched system and recurrent neural networks. Due to the complicated dynamic behavior, the study of switched recurrent neural networks has great significance. By constructing appropriate multiple Lyapunov function according to the different form of switching signal and using Lyapunov stability theory, differential geometry approach together with the descriptor model tranformation approach, the stability criterion under the fixed switching zone is proposed for the switched recurrent neural networks. Based on the stability analysis, the stabilize designing of switching signal for the switched recurrent neural networks is discussed, we search for some switching signal such that the switched recurrent neural networks is stable, some existences and methods of designing for the above switching signal are given. The designing of state estimator for the switched recurrent neural networks is investigated, the conditions for the existence of the full-order state estimator which guarantee the stability of the error system are given,and the simulation is provided to illustrate the effectiveness of the proposed method. By improving average dwell time and constructing the relation of dwell time and delay switching in detection of signal, the stability criterion dependent on the delay of switching signal is provided for the switched recurrent neural networks. The research content is essential for the application of switched recurrent neural networks, which will promote the application of switched recurrent neural networks in the field of high speed signal processing and artificial intelligence.

由于切换递归神经网络具有切换系统和递归神经网络两种系统的特征，使之具有复杂的动态行为，其研究具有重要的意义。本项目在切换递归神经网络已有结果的基础上，根据切换信号不同形式，构造适当的多Lyapunov函数，利用Lyapunov稳定性理论、微分几何法并结合广义模型变换法，给出切换递归神经网络在固定切换域下的稳定性判据；在稳定性分析的基础上，研究切换递归神经网络的镇定切换信号设计，给出实现切换递归神经网络稳定的切换信号的存在条件和设计方法；研究切换递归神经网络的状态估计器设计问题，给出保证误差系统稳定的全阶状态估计器的存在条件，并进行仿真验证其有效性；改进平均驻留时间法，建立驻留时间与切换信号时滞之间的联系，给出切换递归神经网络的切换信号时滞相关稳定性判据，并与已有结果进行比较。项目研究内容属于切换递归神经网络得以应用的基本核心问题，它将促进切换递归神经网络在信号处理和人工智能领域领域的应用。

由于切换递归神经网络具有切换系统和递归神经网络两种系统的特征，使之具有复杂的动态行为。本项目对切换系统和递归神经网络的稳定性进行理论分析。基于H∞滑模控制方法，讨论了级联切换非线性系统的跟踪控制问题。通过解Hamilton–Jacoby不等式，非线性H∞控制方法在第一部分上定义了一个非线性滑模面，并且系统在所定义的滑模面上具有L2增益属性。随后，非线性滑模控制方法被用来实现跟踪任务；通过广义模型变换方法对中立型Hopfield神经网络的状态估计问题进行了研究，给出了保证误差系统稳定的判据；研究了具有泄漏项时滞递归神经网络的稳定性，所考虑的系统具有中立和分布时滞，给出了与中立时滞和分布时滞均相关的稳定性判别准则，数值例子验证了方法的有效性。