拓广下三角结构切换随机非线性系统的控制设计

As an important part of hybrid systems, switched stochastic nonlinear systems take into account the factor of exogenous white-noise，and thus are more applicable and have great significance of theoretical study. Since the introduction of stochastic disturbance and the complexity of the system structure, the dynamic behavior of the switched stochastic nonlinear systems is very complicated, and many basic problems deserve further investigation. For switched stochastic nonlinear systems in lower triangular form, this project will propose several classes of new models and basic analysis tools, based on which the corresponding problems of stabilization, tracking and constrained control will be investigated．Firstly, this project will model several classes of mathematical models for switched stochastic nonlinear systems in generalized lower triangular form with relevant assumptions, and the design methods of switching controllers will be given under arbitrary switching. Secondly, this project will establish the general stability theory of switched stochastic systems, and solve the controller design problems of the considered systems by designing switching signals. The purpose of this project will develop and improve the control theory of the switched stochastic nonlinear systems, and it is of great significance for the control design of the real systems in engineering practice.

切换随机非线性系统，作为混杂系统的重要组成部分，由于考虑了白噪声的影响，具有广泛的应用背景和理论研究意义。但是由于随机噪声的引入以及系统结构的复杂性，使得切换随机非线性系统的动态行为十分复杂，目前仍存在许多基本问题亟待解决。本项目将针对下三角结构切换随机非线性系统，提出几类新的模型，发展一些基本分析工具，研究相应的镇定、跟踪以及受约控制等问题。主要研究内容包括：建立具有拓广下三角结构切换随机非线性系统的若干数学模型并给出相应的假设条件，提出任意切换下的控制设计方案；发展一般的切换随机系统稳定性理论，通过设计切换信号解决所研究系统的控制设计问题。项目研究将完善和发展切换随机非线性系统的控制理论，同时对工程实践具有指导意义。

本项目研究了几类具有拓广下三角结构不确定切换非线性系统的控制器设计与稳定性分析问题，通过灵活的应用近似逼近技术以及Backstepping设计方法，得到了一些比较重要的理论研究成果。主要的研究内容包括：(1) 考虑了一类具有拓广下三角结构切换随机非线性系统的自适应输出反馈控制问题，利用自适应控制、Backstepping技术结合神经网络估计以及平均驻留时间方法，给出了控制器的设计方法。(2) 研究了一类含有输入时滞的多输入多输出切换非线性系统的自适应跟踪控制问题，首次基于多Lyapunov函数方法给出了该类系统自适应跟踪控制问题可解的充要条件。(3) 对于一类含有状态时滞和量化输入的纯反馈切换非线性系统，应用变量分离技术、动态面控制以及Lyapunov–Krasovskii泛函方法给出了设计方案，并基于Lyapunov稳定性理论讨论了闭环系统的稳定性和收敛性问题。截止目前，项目组在IEEE Transactions on Neural Networks and Learning Systems、IEEE Transactions on Cybernetics、IEEE Transactions on Systems, Man, and Cybernetics: Systems等国际SCI期刊与会议上发表论文(含录用)8篇，其中在IEEE汇刊上发表论文5篇(长文4篇，短文1篇)，其它SCI期刊(Journal of the Franklin Institute)论文1篇，EI收录的国际会议论文2篇。