受扰非线性切换系统的有限时间有界控制理论与应用研究

Finite time bounded theory of switched systems can provide the qualitative information about the stability of switched systems, and also yields quantitative information about their transient behaviors. Because finite time boundedness accords with actual engineering demand better than that of Lyapunov stability, it has aroused widespread concern in theory and engineering. However，most of existing results are limited to the study of switched linear systems, and the research on switched nonlinear systems is still in its initial stage. The purpose of this project is to establish finite time bounded theory about control, observation and implementation for perturbed switched nonlinear systems in a constructive way. There are five parts included in this project. First, finite time state feedback bounded theory of switched nonlinear systems is established. Then, finite time bounded observer design method is proposed. Combining the observers and the state feedback controllers, finite time bounded output feedback controllers of switched nonlinear systems are designed. Furthermore, finite time disturbance observation and compensation method is proposed and finite time bounded composite control algorithm is developed. Moreover, sample-data control theory and accuracy analysis for the above developed algorithms are considered. On this basis, the proposed methods are applied to the design of steering control system of agricultural machinery, and the digital implementation technologies and the rules of tuning parameters are studied. The research of this project will not only help to improve and perfect finite time bounded theory of perturbed switched nonlinear systems, but also provide the basis to the finite time bounded controller design and implementation for practical systems.

切换系统有限时间有界理论不仅可定性分析系统稳定性，且能给出系统暂态的定量信息。由于其比Lyapunov稳定更契合实际工程需求，因此在理论和工程界引起了广泛关注。但是，现有成果大多限于线性切换系统的研究，非线性切换系统的研究尚处于初步探索阶段。本项目旨在利用构造性方法，建立受扰非线性切换系统有限时间有界的控制、观测和实现理论，主要包括：(1)建立非线性切换系统状态反馈有限时间有界理论；(2)提出有限时间有界观测器设计方法，结合状态反馈控制，设计有限时间有界输出反馈控制器；(3)提出有限时间扰动观测和补偿方法，设计有限时间有界复合控制算法；(4)研究上述方法的采样控制理论，讨论算法实现和控制精度；(5)将上述成果应用于农机转向控制系统设计，研究调参规律和数字化实现。本项目的研究，不仅有助于发展和完善非线性切换系统有限时间有界理论，而且能够为实际系统有限时间有界控制器设计和实现提供依据。

切换系统有限时间有界理论不仅可定性分析系统稳定性，且能给出系统暂态的定量信息，比Lyapunov稳定更契合实际工程需求，因此引起了广泛关注。但是，目前非线性切换系统的研究尚处于初步探索阶段，其分析和综合问题有待进一步深入研究。因此，本项目主要目标是建立受扰非线性切换系统有限时间有界的控制、观测和实现理论。.本项目按照原定计划，顺利地完成了项目预期目标。首先，理论研究方面，分别利用构造性方法和系统化手段，初步解决了切换系统有限时间有界的稳定性分析和反馈控制设计问题，给出了状态反馈控制器和状态观测器的设计方法；给出了有限时间有界和具有有限时间加权L2增益的充分条件，定量分析了切换系统有限时间的扰动抑制能力；给出了切换系统有限时间有界的等周期采样控制设计方法，解决了采样间隔内控制器和子系统不匹配等理论难题；给出了具有定量输出约束的切换系统的系统化控制设计方案。其次，实际应用方面，将本项目所提出的理论，应用于农机转向控制和蔬菜育苗流水线控制设计中，给出了系统性能的定量分析方法。.本项目的研究，不仅有助于发展和完善非线性切换系统有限时间有界理论，为有限时间有界控制器设计和实现提供理论依据，而相关理论在农业机械控制中的实用验证，将进一步推动农业生产的自动化程度。