一类随机反应扩散神经网络的周期间歇采样控制  

Periodically Intermittent Sampled-Data Control of a Class of Stochastic Reaction-Diffusion Neural Networks

作　　者：罗世贤[1] 陈武华[1] 

机构地区：[1]广西大学数学与信息科学学院,南宁530004

出　　处：《系统科学与数学》2017年第3期652-664,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助项目(61573111);国家自然科学基金重点项目(61633011);广西自然科学基金资助项目(2015GXNSFAA139003)资助课题

摘　　要：基于周期间歇采样控制策略研究了一类随机反应扩散神经网络的镇定问题.所提出的镇定方案基于空间采样并关于时间间歇,即采样控制只在"工作时间"被激活,而在"工作时间"的每个时刻,只在空间中的有限个点对状态采样.引入分段Lyapunov函数,并利用Wirtinger积分不等式充分发掘扩散项的镇定作用,建立了系统全局均方指数稳定的充分条件,该条件定量揭示了控制周期、控制宽度、空间采样区间的上界之间的关系,基于稳定性条件,给出了周期间歇采样控制器的参数化设计方法.最后通过数值例子验证了所提出方法的有效性.In this paper, the stabilization problem of a class of reaction-diffusion stochastic neural networks via periodically intermittent sampled-data control is studied. The proposed stabilization scheme is based on the assumption that the state is sampled in space variables and the control action is intermittently activated in time. That is, the sampled-data control is only activated in “work time”, and at each moment during “work time”, the measurement of the states is taken in a finite number of fixed sampling points in the spatial domain. By introducing a piecewise Lyapunov function combined with the technique of applying Wirtinger＇s inequality for exploring the stabilizing role of the reaction-diffusion term, a sufficient condition for globally mean-square exponential stability is developed in terms of linear matrix inequalities. The obtained condition establishes a quantitative relation among the control period, the control width, and the upper bound on the spatial sampling intervals. Based on the stability criterion, a parameterized representation of the periodically intermittent sampled-data controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theoretical results.

关 键 词：反应扩散 随机神经网络 采样控制 间歇控制 分段LYAPUNOV函数 线性矩阵不等式 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程] TP273[自动化与计算机技术—控制科学与工程]