具有正特性的切换模糊系统的控制设计

This project intends to investigate the control design problem of switched fuzzy systems with positive performance (called switched positive fuzzy systems below). Exhibiting features of switched systems, positive systems and fuzzy systems, switched positive fuzzy systems are more complicated hybrid systems. In practice, switched nonlinear positive systems can be more precisely described by switched positive fuzzy systems. Only a few results on such issues have been reported up to now. In this project, firstly, based on the (two-layer) multiple co-positive Lyapunov functions method, the stabilization problem is studied for switched positive fuzzy systems, and controllers and a switching law are designed; Next, we investigate the stabilization and H∞ control problem of switched positive fuzzy systems with saturating actuators, and design a switching law. Feedback controllers and anti-windup compensation gains are designed based on the convex hull technique and the anti-windup technique, respectively. Finally, the problem that a switched fuzzy system can become a positive system is studied. The project shows the interrelation among controllers, switching laws and positive performance, which play different roles in the stabilization of switched positive fuzzy systems. The results will be expected to apply to control design of practical switched nonlinear positive systems.

本项目研究具有正特性的切换模糊系统（下简称切换正模糊系统）的控制设计问题。切换正模糊系统同时兼备切换系统，正系统和模糊系统的特征，它能够准确刻画实际的切换非线性正系统，是一种极为复杂的混杂系统。目前，对其研究结果尚十分有限。在本项目中，首先，利用（双层）多余正Lyapunov函数方法，研究切换正模糊系统的镇定问题，并双重设计控制器和切换信号；其次，研究具有执行器饱和的切换正模糊系统的镇定及H∞控制问题，设计切换信号的同时，分别采用凸包技术和抗饱和技术设计反馈控制器和抗饱和补偿器；最后，研究切换模糊系统正性化的问题。本项目揭示控制器、切换信号和正特性之间的相互关联，及其在切换正模糊系统镇定中所起的不同作用。研究成果可望应用于实际切换非线性正系统的控制设计中。

本项目主要针对切换模糊系统进行鲁棒控制的研究，提出几类了基于切换策略的控制设计的方法。项目组成员共发表标注基金号的论文4篇，其中2篇被SCI收录，2篇被EI收录，在投论文2篇，申请专利2项。项目负责人罗金鸣成功获得辽宁省教育厅项目（2021）。 .本项目的主要创新工作集中在如下几方面：1)基于切换理论研究一类微电网系统的切换控制问题。针对微电网运行的两种模式，在设计切换信号下，得到闭环切换模糊系统的稳定性条件，同时给出控制器的设计方法，保证了微电网切换模型稳定运行；2）分别针对状态反馈带记忆功能和状态不可测两种情形，基于（双层）多Lyapunov函数方法研究切换模糊系统鲁棒镇定和H无穷控制问题，并分别设计了带记忆功能的控制器和输出反馈控制器；3）在具有网络时延和数据包丢失的网络环境中，研究不确定非线性网络控制系统的鲁棒容错控制问题。将非线性网络控制系统转化为含有不确定性的T-S模糊时滞模型，在考虑部分执行器失效的情况下，利用积分不等式和时滞依赖的分析方法，得到了闭环系统的鲁棒稳定性条件。