仿射T-S模糊系统的滑模控制及通用模糊滑模控制器研究

In recent years, there have been rapidly growing interests in systematic stability analysis and synthesis of fuzzy control systems. Among various model-based fuzzy-control strategies, the method based on Takagi-Sugeno (T-S) fuzzy models, or the so-called fuzzy-dynamic models, is well suited to the model-based nonlinear control. It has been shown that T-S affine dynamic models with offset terms have much improved function approximation capabilities than T-S fuzzy systems with linear local models. On the other hand, as an effective robust control strategy, sliding mode control (SMC) has various attractive features such as strong robustness and fast response. Nevertheless, it is noted that most of the existing sliding mode control design results were developed only for T-S fuzzy systems with linear local models based on common Lyapunov functions and there are few results on sliding mode control for T-S fuzzy affine systems. It is also worth mentioning that the analysis and synthesis procedures of sliding mode controllers for T-S fuzzy affine systems are generally more complex than T-S fuzzy systems with linear local models. In this project, based on piecewise Lyapunov functions combined with some elegant matrix analysis and convexifying techniques, we will investigate and develop novel approaches to analysis and synthesis of synchronized/non-synchronized sliding mode controllers for T-S fuzzy affine dynamic systems via state feedback and output feedback, and will also address the universal fuzzy sliding model controller problem for several classes of multi-input multi-output nonlinear systems based on T-S fuzzy affine dynamic models. In addition, we will select a number of benchmark nonlinear systems such as space robots as test beds to evaluate the validation and performance of the proposed analysis and synthesis approaches. Comparison with other existing analysis and design techniques will also be conducted. The outcome of this project is expect to enrich theoretical foundation on T-S fuzzy model-based sliding mode control methodologies, and, in turn, the proposed approaches will provide control engineers in practice with more solid analysis and design tools.

基于T-S模糊模型的模糊控制方法是针对非线性系统控制的一种非常有效的方法。相对于传统的不含仿射项的线性T-S模糊模型，仿射T-S模糊模型具有更强大的非线性逼近能力以及实际应用背景。另一方面，滑模控制因其具有强鲁棒性和良好的动态品质受到了广泛关注。目前针对T-S模糊系统的滑模控制研究大多是基于传统的线性T-S模糊模型以及公共Lyapunov函数，而对于更一般的仿射T-S模糊系统的滑模控制以及通用模糊滑模控制器研究，尚少有相关成果报道。本项目基于分段Lyapunov函数以及各种矩阵分析技术和参数解耦技巧，研究仿射T-S模糊系统的各类状态反馈、输出反馈同步以及非同步滑模控制；针对几类非线性系统，研究其通用模糊滑模控制器的存在条件和求解算法。本项目的部分理论将在空间机器人的控制中进行尝试性应用。本项目的宗旨是提出一套较为完整的仿射T-S模糊系统滑模控制理论，并为工程技术人员提供较为实用的设计方法。

本项目基于分段Lyapunov函数以及各种矩阵分析技术和参数解耦技巧，研究了仿射T-S模糊系统的各类状态反馈、输出反馈同步以及非同步滑模控制器设计问题；并针对几类非线性系统，研究其通用模糊滑模控制器的存在条件和求解算法。本项目的部分理论成果已在机器人系统的控制中进行尝试性应用。本项目的宗旨是提出一套较为完整的仿射T-S模糊系统滑模控制理论，并为工程技术人员提供较为实用的设计方法。基于此项目，在国际SCI期刊上发表论文40篇(其中包括21篇IEEE Transactions系列汇刊论文)。