基于非精确测量变量反馈的非线性输出调节研究

Output regulation is one of the most significant modern control problems. Currently, this problem majorly focuses on systems with arbitrary parametric uncertainties, arbitrary external disturbances, as well as the complex nonlinear dynamics. The internal model principle has shown to be the unique method for handling this problem. However, a stringent restriction for the traditional internal model is that the system variables used for the feedback should be exactly measured, leading to the rigorous condition for the practical implementation. In view of this situation, by taking into account the requirement of some other engineering fields such as the internet, communication, and instrument, in this project, we aim to establish a novel systemic framework for the nonlinear output regulation with the coarse measurement feedback. Specifically, we would like to explore the internal model principle with the coarse measurement feedback in both the centralized and the distributed versions, so as to effectively circumvent the hurdles encountered by inexact feedback variables. By making use of these novel internal models, we then solve in sequence the centralized global practical output regulation problem for two typical classes of nonlinear systems and the cooperative global practical output regulation problem for two typical classes of nonlinear multi-agent systems. We also bring the new insight of the output regulation theory from the view point of the coarse measurement feedback, and therefore achieve the deep development of this theory. Finally, we will use our theoretical results and novel methods for solving several practical cooperative control problems, such as rendezvous and formation for multiple mobile robots. This achievement strictly enlarges the real application range and hence makes theory combined with practice more compactly.

输出调节是现代控制的核心问题之一。当前，该问题的重点研究对象是具有不确定性参数、外界干扰各类复杂非线性系统。内模原理是该问题唯一行之有效的控制方法。然而，传统的内模控制器严格要求反馈变量要精确测量，对物理实现要求严苛。基于此现状，综合互联网、通信、精密仪器等多领域工程实际需求，本项目拟建立一套系统化的基于非精确测量变量反馈的非线性输出调节理论体系，分别发展此条件下的集中式与分布式内模控制方法，从本质上突破现有内模对非精确反馈变量的技术瓶颈。进而，运用新型内模，依次解决两类标准型单一非线性系统的集中式全局实践输出调节问题与两类标准型非线性多自主体系统协作式全局实践输出调节问题，从非精确测量变量反馈角度对非线性输出调节进行全新诠释与求解，实现输出调节理论的跨越式发展。最后，本项目将同时实现理论成果在机器人组聚类、编队等实际控制中的应用，拓广内模原理的应用对象与范围，实现理论与应用的紧密结合。

输出调节是现代控制的核心问题之一。该问题的重点研究对象是具有不确定性参数、外界干扰的各类复杂系统。传统的输出调节控制器严格要求反馈变量被精确测量，对物理实现要求严苛。基于此现状，综合互联网、通信、精密仪器等多领域工程实际需求，本项目旨在建立一套系统化的基于非精确测量变量反馈的输出调节理论体系，分别发展此条件下的集中式与分布式控制方法，从本质上突破现有内模对非精确反馈变量的技术瓶颈。沿此方向指引，本项目深入探讨了各类基于观测器输出反馈、量化反馈、采样反馈等非精确测量变量反馈的单个体系统镇定控制、输出调节，多智能体系统一致性、协作式输出调节等问题；分别建立了在非精确测量变量反馈条件下的多智能体系统分布式前馈控制框架体系与分布式内模控制框架体系；先后发展了广义不变集定理、单值矩阵分析等新型切换与混杂系统稳定性分析工具、（积分）输入状态镇定、分布式鲁棒与自适应反步递归迭代等新型控制算法、基于量化、采样的分布式内模与分布式观测器、基于数据学习的自适应最优输出反馈控制等新型控制技术；依次实现了理论成果在高超音速飞行器跟踪、智能微电网分布式功率分配、轮式移动机器人组编队聚类等实际问题的应用。所获研究成果从非精确测量变量反馈角度对非线性输出调节进行全新诠释与求解，实现了输出调节理论的有效发展。在研究计划资助下，项目组成员共计发表（含录用）国际期刊与会议论文26篇，其中SCI收录论文9篇，其中系统控制领域两大国际权威期刊IEEE Transactions on Automatic Control与Automatica合计6篇，信息领域国内卓越期刊SCIENCE CHINA Information Sciences合计2篇。录用学术专著一本（出版社：Springer Nature Switzerland AG）。先后获ICCA2019最佳论文候选奖、CCC2021张贴论文奖。