基于微分包含式近似的多不连续集值映射滑模变结构滤波器的实现理论

滑模变结构滤波器具有高跟踪性、高鲁棒性等优点，在控制领域有广泛的应用前景。本项目旨在前期研究的基础上，研究滑模变结构滤波器的亟待解决的三个关键问题：1)滤波平滑度和跟踪速度的改善问题；2)复杂滑模变结构系统的离散化问题；3)离散时间高阶滑模变结构系统的收敛性证明问题。针对1)问题，研究具有多个不连续集值映射结构的控制律，突破传统研究仅采用单一不连续集值映射结构的局限。针对2)问题，采用微分包含式近似方法，研究完全保留连续时间特性、无抖振、无超调的离散化，突破传统离散化方法的瓶颈问题。在此基础上，针对3)问题，采用离散李雅普诺夫方法，研究离散时间高阶滑模变结构系统的收敛性，突破传统研究仅考虑连续时间收敛性的局限。最后，通过位置、速度、Admittance等控制实验，评估研究成果的优越性。研究成果将为滑模变结构滤波器及其相关技术关于理论与实践结合的研究提供崭新的思路及科学的理论依据。

In feedback control of mechatronic systems, sliding mode filters have been recognized as one of the most effective tools for removing noise owing to their tracking accuracy, robustness. As an extension of our previous work, this research project aims to solve the following three key problems in designing and implementing sliding mode filters: 1) improvement of filtering smoothness and suppression of tracking delay, 2) discretization of complex sliding mode systems, and 3) stability of discrete-time high-order sliding mode systems.. First, the research seeks to develop a new generation of sliding mode filters featuring multiple discontinuous set-valued mappings for avoiding drawbacks of conventional methods that only include a single mapping. Then, based on differential inclusion approximation, the research dedicates to provide a general framework of discretizing complex sliding mode systems that avoids chattering and overshoot without loosing inherent characteristics of sliding mode systems. After that, by applying the discrete-time Lyapunov method, the research proceeds to investigate stability of discrete-time high-order sliding mode systems for clarifying the influences of sampling time, disturbance and noise on convergence accuracy. Finally, the research intends to validate the advantages of the developed systems through feedback control of mechatronic systems.. The results of this research will provide valuable insights and theoretical supports for the future development of sliding mode filtering technology.