隶属度函数部分未知的T-S模糊系统有限频控制器设计

Due to the existence of unknown parameters and uncertainties, it is difficult to obtain accurate membership functions in the process of modelling of T-S fuzzy models, which obviously increase the difficulty of controller design. Also, the external inputs always belong to finite frequency domains, which leads to the existing full frequency controller design methods may deteriorate the performance of closed-loop systems. To achieve the satisfactory performance of closed-loop systems, this item is concerned with the finite frequency controller design for T-S fuzzy systems with partially unknown membership functions and finite frequency external inputs. Firstly, considering the case that the system states are all available, based on the time domain interpretations of finite frequency performance, it will use switching techniques to estimate the unknown membership functions, and state feedback controller design approach is then given. If the system states are unavailable, the dynamic output feedback controller design approach will be further studied. In addition, the proposed finite frequency controller design method will be extended to the T-S fuzzy systems with time-delay and the ones with input saturation. Finally, the finite frequency filter design method will be considered based on switching techniques. This research item is of great importance from either the development of robust control theory point of view or the improvement of finite frequency performance of practical control systems point of view.

在T-S模糊模型的建模过程中，受未知参数以及不确定性等未知因素影响隶属度函数往往很难精确获得，这导致控制器设计变得非常困难和复杂。同时，实际系统的外部输入通常为有限频信号，因此在全频域内设计控制器会导致闭环系统性能下降。本项目旨在针对隶属度函数部分未知的T-S模糊系统，综合考虑外部输入的频域特性，在有限频范围内研究控制器设计方法以提高闭环系统性能。首先，考虑系统状态可测的情形，拟结合有限频性能分析结果引入切换机制对隶属度函数未知部分进行估计，进而研究有限频状态反馈控制器设计方法。对系统状态不可测的情形，进一步研究有限频动态输出反馈控制器设计方法。其次，拟将所提出的有限频控制器设计方法推广至带有输入饱和与带有时延的T-S模糊系统。最后，研究基于切换技术的有限频滤波器设计方法。本项研究工作的开展不论是对鲁棒控制理论本身发展，还是对改进实际系统的有限频性能都具有重要意义。

本项目针对隶属度函数部分未知的T-S模糊系统，综合考虑外部输入的频域特性，在有限频范围内研究控制器设计方法以提高闭环系统性能。项目结合有限频性能分析结果引入切换机制对隶属度函数未知部分进行估计，进而给出有限频状态反馈控制器设计方法。进一步，利用系统输出研究有限频动态输出反馈控制器设计方法。同时，将所提出的有限频控制器设计方法应用于T-S模糊系统的故障检测问题。最后，研究基于切换技术的有限频滤波器设计方法，并且部分理论结果应用于实验室现有的倒立摆实验仿真平台，验证了所提出方法的有效性和实用性。本项研究工作的开展不论是对鲁棒控制理论本身发展，还是对改进实际系统的有限频性能都具有重要意义。