具有马尔科夫类跳变的中立型神经网络的稳定性分析与控制器设计研究

本项目基于随机泛函微分方程理论和控制理论，以马尔科夫类跳变传输率的不确定性和模态驻留时间的分布属性以及时变时滞的不同类型为实际背景，拟用泛函分析方法及相关运算技巧，系统地开展对具有马尔科夫类跳变的中立型神经网络的稳定性分析和控制器设计的研究，达到改进现有研究结果的保守性和充实中立型神经网络的研究内容的目的。. 本项目主要研究内容包括：利用凸优化理论和代数学原理，结合不等式处理技巧，研究得到保守性低的新积分不等式；研究得到保守性低的时滞依赖矩稳定性和几乎必然稳定性条件；研究全阶或降阶的扩展耗散性状态估计问题；研究扩展耗散性异步控制器设计问题；研究模态驻留时间的分布属性与传输率的不确定性对具有马尔科夫类跳变的中立型神经网络的稳定性与控制器设计的影响问题。. 通过本项目的研究，有望能够完善中立型神经网络的理论体系，拓展中立型神经网络的应用领域，推动混杂动力学系统的分析与设计研究

Based on the theory of stochastic functional differential equations and control theory, setting the uncertainty of the model transmission probability in Markov’s like jump, the property of the dwell-time distribution of the model in Markov’s like jump, and the different types of time-varying delays as actual background, using functional analyzing skills and relevant operation technique, this project systematically studies the stability and control of neutral neural networks with Markov’s like jump, aiming to improve the conservatism of the existing results as well as enrich and complete the researching contents of neutral neural networks. . The major studying contents of this project include: studying new integral inequality based on the convex optimization theory and algebra principle, and combined with the inequality technique, investigating the less conservative delay-dependent moment and almost sure stability condition, discussing the issue of full-order or reduced-order extended dissipative state estimation, working on the problem of extended dissipative asynchronous control, analyzing the problem of the influence which includes the property of the model dwell-time and the transmission probability of the jump to neutral neural networks with Markov’s like jump. . Through the research of this project, we are expecting to promote the theoretical system of neutral neural networks, as well as to enrich practical field of neutral neural networks and to enhance the analysis and research of hybrid dynamical system.