复杂随机切换系统的可靠性控制与滤波器设计

Stochastic switched system is a kind of important hybrid system, which is widely used in interconnected systems, aircraft control systems and intelligent systems.This project aims to investigate the stability and reliable control design problems of stochastic switched system under the influence of the influence of many factors including time delay, switching signal disturbances, uncertain parameters and multiple faults. The main research contents are as follows: (1)Based on the stochastic process theory and so on, the stochastic switched delay differential equations are established considering the disturbances of switching signals. The appropriate time and rate of change are designed to ensure the stability of the system. (2)By constructing a new piecewise Lyapunov functional on the basis of the Ito formula and the martingale theory, we will design H/infinity reliable feedback controller to ensure the robust stability of stochastic switched systems with delay under switching signal perturbations. (3) Under output disturbances and multiple faults occur randomly and using vertebral complementarity linearization method, we design H/infinity filter. Through the research of this project, we hope to perfect the theoretical system of stochastic switched dynamical systems, open up the application field of stochastic switching system with time delay, and promote the analysis and research of hybrid dynamic systems.

随机切换系统是一类重要的混杂系统，被广泛应用于互联系统、飞行器控制系统以及智能系统等方向。本项目围绕具有时滞、切换信号受扰、参数不确定以及多重故障等多因素影响下的随机切换系统的稳定性和可靠控制设计等问题进行研究。主要研究内容为：(1)根据随机过程等理论，充分考虑切换信号受扰时，建立随机切换的时滞微分方程模型，设计恰当的时间变化率和模型变化率，确保系统的稳定性；(2)构造新的分段Lyapunov泛函结合伊藤公式及鞅理论等方法，设计H无穷可靠反馈控制器，确保在切换信号扰动下时滞随机切换系统的鲁棒稳定性；(3)在未知输出扰动和多重故障随机发生时，采用椎体互补线性化方法，设计H无穷滤波器。通过本项目的研究，期望能完善时滞随机切换动力系统的理论体系，开拓时滞随机切换系统的应用领域，推动混杂动力学系统的分析与研究。

随着传感器、执行器及互联网技术的不断进步，以及智慧化城市建设的提出，对智能系统的稳定性和安全性要求越来越高，所以需要对网络、数据和图像进行高效和最优的处理。（1）研究了具有时滞和切换不确定的随机神经网络的稳定性和控制器设计，通过线性矩阵不等式、凸不等式处理方法以及随机Lyapunov方法，设计出随机切换系统最优的控制器。（2）提出了双注意融合模型使用交互式注意力模块，同时考虑简单的操作融合空间和时间维度成功导出可以区分的EEG信号的特征。（3）提出了一种基于最大相关熵准则的低秩矩阵分解模型来处理半监督场景中的特征学习问题，该方法能够较好的保持样本的全局重构信息，同时自适应的学习样本的局部结构关系来进行特征学习。本项目讨论的问题和方法可以拓展来解决机器学习和人工智能中的其他相关应用，因此本项目的研究成果具有较高的应用价值.

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