非线性奇异摄动切换系统的模糊抗饱和控制

Singularly perturbed switched systems can be used to describe a wide class of complex systems with switching characteristics and multi-time-scale characteristics, such as power electronic systems, and robot systems. Control of singularly perturbed switched systems is an open problem because the classical singular perturbation theory has not been proved for general switched systems. Most of the existing results for singularly perturbed switched systems are limited to linear systems and cannot deal with nonlinearities and actuator saturation. This project will study fuzzy anti-windup control for nonlinear singularly perturbed switched systems. The main topics are as follows: (1) by introducing a virtual dynamic control input and using T-S fuzzy modeling methods, slow and fast subsystems based on T-S fuzzy models are established to approximate the nonlinear singularly perturbed switched systems; (2) the classical singular perturbation theory will be generalized to switched systems and the relationship between stability of the singularly perturbed switched systems and that of the slow and fast subsystems will be established, by which T-S-fuzzy-model based controller and anti-windup compensator design methods, and stability analysis approaches for the closed-loop systems will be investigated. This research will promote the development of control theory and technology for singularly perturbed switched systems.

奇异摄动切换系统能够较为科学地描述众多具有切换特性和多时间尺度特性的复杂系统，例如电力电子系统、机器人系统等。由于传统的奇异摄动理论针对切换系统尚无一般性结论，奇异摄动切换系统的控制问题是控制领域的一个难题。现有研究大多局限于线性系统，无法处理非线性和执行器饱和特性。本项目研究非线性奇异摄动切换系统的模糊抗饱和控制方法，具体内容包括：(1) 引入虚拟动态控制输入，利用T-S模糊建模方法建立具有执行器饱和的非线性奇异摄动切换系统的慢、快子系统T-S模糊模型；(2) 把传统奇异摄动理论拓展到切换系统，揭示奇异摄动切换系统稳定性与其慢、快子系统稳定性的关系，进而研究基于慢、快子系统T-S模糊模型的控制器和抗饱和补偿器设计方法以及闭环系统稳定性分析方法。研究成果将推动奇异摄动切换系统控制理论和技术的发展。

奇异摄动切换系统能够较为科学地描述众多具有切换特性和多时间尺度特性的复杂系统，例如电力电子系统、机器人系统等。由于传统的奇异摄动理论针对切换系统尚无一般性结论，奇异摄动切换系统的控制问题是控制领域的一个难题。现有研究大多局限于线性系统，无法处理非线性和执行器饱和特性。本项目研究非线性奇异摄动切换系统的模糊抗饱和控制方法，并取得了重要成果：1)针对具有执行器饱和的非线性奇异摄动切换系统，建立了基于广义系统模型的T-S模糊模型和低阶慢、快子系统 T-S模糊模型；2) 提出了基于T-S 模糊模型的非线性奇异摄动切换系统的控制器设计方法；3)建立了抗饱和补偿器设计方法以及闭环系统稳定界和吸引域的估计方法。在本项目的资助下共发表学术论文17篇，申请发明专利3项；培养研究生9人。