【作者】 苏卫卫；

【导师】 陈一鸣；

【作者基本信息】 燕山大学 ， 计算数学， 2008， 硕士

【摘要】 神经网络是一种智能控制技术,它能模拟人的智能行为,能解决传统自动化技术无法解决的许多复杂的、不确定的非线性的自动化问题。因而近几十年来,对神经网络的研究引起学术界的广泛关注。时滞神经网络的理论与应用研究是目前国际上神经网络领域的前沿课题之一。时滞不仅是反映了人工神经网络中放大器有限的开关速度等硬件实现,也是为了更好地模拟生物神经网络的延时特性,同时也是解决某些实际问题的需要。论文基于Lyapunov稳定性理论和线性矩阵不等式技术,研究了几类时变时滞神经网络系统的稳定性问题,给出了保证系统全局稳定的充分条件,与已有的结果相比,降低了保守性。首先,论文研究了一类细胞型神经网络系统的鲁棒稳定性问题,以线性矩阵不等式的形式给出了保证系统全局渐进稳定和指数稳定的充分条件,所给的准则解除了对时变时滞变化率的限制,从而降低了保守性,并通过数值例子验证了结论的可行性和有效性。其次,论文针对一类随机型神经网络系统,应用随机分析技术,就范数有界不确定性和区间型不确定性两种情况,给出了保证系统全局指数稳定的充分条件。接着,研究了一类中立型随机神经网络系统的鲁棒稳定性问题,给出了保证系统稳定的充分条件,仿真实例进一步验证了结论的有效性。最后,针对一类带有分布时滞的随机Cohen-Grossberg神经网络系统,给出了保证系统全局渐进稳定的时滞依赖的充分条件,与已有的结果相比适用范围更广,保守性更小。更多还原

【Abstract】 Neural networks is a kind of intelligent control technology, which can simulate human being’s intelligent behavior, solve many complicated and nondeterministic nonlinear automation problems not settled by traditional automaton technology. Therefore, during the last several decades, the study of neural networks has aroused the general interest of academic field. The theory and application of the neural netwotks with time-delay is one of the international foreland problems at present. The time-delay not only has reflected the hardware reality such as limited switch speed of amplifier in the artificial neural networks, but also better simulates the time-delay character of biology neural networks. At the same time, it is the need to solve certain actual problem.Based on Lyapunov stability theory and linear matrix equality (LMI) technology, the stability analysis of several neural networks with time-varying delays is investigated in this thesis. Sufficient conditions are given in terms of LMIs to ensure the stability of neural networks. Compared with some existing results, the criteria obtained in our paper are less conservative.Firstly, the robust stability problem for a class of uncertain cellular neural networks with norm-bounded uncertainties is considered in this paper. The conditions are proposed to guarantee the asymptotic and exponential stability of neural networks, which are dependent on the time-varying delays. And we don’t need the restriction that the derivative of time-varying delay is less than one. A numerical example is given to illustrate the effectiveness and improvement over some existing results.Secondly, the global exponential stability is investigated for a class of stochastic neural networks with time-varying delays and norm-bounded uncertainties or interval uncertainties. Based on Lyapunov stability theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, exponential stability of the addressed system in the mean square for all admissible parameter uncertainties. A numerical example is given to illustrate the effectiveness and improvement over some existing results.Thirdly, the global asymptotic stability is investigated for a class of neutral stochastic neural networks with time-varying delays and norm-bounded uncertainties. Based on Lyapunov stable theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, asymptotic stability of the addressed system in the mean square for all admissible parameter uncertainties. A numerical example is given to illustrate the effectiveness of our results.In the end, the problem of robust asymptotic stability analysis of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays is studyed. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technology, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. A numerical example is given to demonstrate the effectiveness and improvement of our results.更多还原