二维离散切换系统基于事件驱动的分析与控制研究

With the development of the modern industry and computer technology, multiple variables are used to describe the practical systems and signals. Thus, the two-dimensional (2D) systems theory becomes one of the most important research areas in the control theory and applications. The dynamics of 2-D systems exists extensively in fields of the power systems, heat transition process, image and signal processing, robot control, aircraft control and so on. In practice, abrupt changes or sudden faults may occur to the 2D systems, which can be modelled as the switched parameters. However, little attention has been paid to this phenomenon in the obtained 2D system theory. The feature of two-dimension and switched parameters lead to the complex system structure and it becomes very challenging to investigate the stability analysis and control problems for the discrete-time 2D switched systems. Combining with the discrete-time 2D system theory and the switched system theory, the stability analysis, stabilization and sliding mode control problems are studied in this project via the 2D bounded real lemma, dwell time technique and event-triggered strategy; The obtained theoretical results are further implemented tentatively on the renewable energy power systems and the signal processing. This project aims to develop a systemic and comprehensive theory for stability analysis and control of the discrete-time 2D switched systems, and provide technical support for the engineers in real world applications.

随着现代工业和计算机技术的迅速发展，很多系统和信号需要用多变量多维度来刻画，因此二维(Two-dimensional, 2D)系统理论成为控制系统理论的一个重要研究领域，其动力学系统广泛存在于电力系统、热转换过程、图像和信号处理、机器人控制、飞行器控制等。实际二维系统中经常出现结构突变或突发故障（常建模为跳变参数），但现有的二维系统理论少有考虑参数跳变情况。二维系统沿两个维度更新的特性和跳变参数的双重影响导致系统结构异常复杂，其稳定性分析和控制问题极具挑战性。本项目针对二维离散切换系统，结合二维系统理论和切换系统理论，利用有界实引理、驻留时间技术和事件触发策略，解决其稳定性分析和控制器设计等问题，将部分理论成果应用到多能源电力系统控制及多维信号处理问题中。本项目旨在建立一套较为完善的二维离散切换系统的分析与控制器设计方法的理论体系，为相关工程技术人员提供理论依据和技术支持。

随着现代工业和计算机技术的迅速发展，很多系统和信号需要用多变量多维度来刻画，因此二维(Two-dimensional, 2D)系统理论成为控制系统理论的一个重要研究领域。实际二维系统中经常出现结构突变或突发故障，二维系统沿两个维度更新的特性和跳变参数的双重影响导致系统结构异常复杂，其稳定性分析和控制问题极具挑战性。本项目针对二维离散切换系统，结合二维系统理论和切换系统理论，利用有界实引理、驻留时间技术和事件触发策略，解决其稳定性分析和控制器设计等问题，建立了一套较为完善的二维离散切换系统的分析与控制器设计方法的理论体系，为相关工程技术人员提供理论依据和技术支持。依托本项目发表（含录用）国际SCI期刊论文17篇（其中一作/通讯15篇），包括控制领域顶级期刊Automatica论文3篇，IEEE TAC、IEEE TIE、IEEE TSMCS等。已发表的研究成果得到国内外学者的引用及推广。基于上述部分研究成果，项目负责人获2021中国自动化学会自然科学二等奖（排名第1）、入选国家青年人才支持计划、山东大学齐鲁青年学者特聘教授、获IEEE Senior Member、入选山东省高等学校青年创新团队（团队负责人）。