复杂动态网络下基于多重一致性滤波的分布式观测器设计

The design of distributed observers is an interdisciplinary at the cross-point of multi-agent systems and multi-source information fusion, which proposes a new research paradigm on the analysis and prediction of the operation of the complex systems. At present, most of the design algorithms of distributed observers are based on complex high-dimensional linear matrix inequality, which constrains its application in real engineering system causing by the complicated and conservative calculation process. By introducing some auxiliary variables basing on sampling mechanism, this project aims to establish framework of distributed observers with multiple consensus filtering. By analyzing the design schemes of distributed observers with fixed networks, dynamical networks and nonlinear systems step by step, this project will reveal the internal mechanism of reducing complexity and conservatism of parameters design determined by multiple consensus filtering, find the influence of complex dynamical networks on the parameters of observers and convergence performance, and adaptation method to deal with the global detectable condition in nonlinear systems. The design algorithm of parameters and analysis procedure of tracking performance will be both greatly simplified，which lays important foundation for the control and intervention of complex systems with incomplete states information. The applicant has published 7 IEEE Transactions papers and 1 ESI highly cited paper on the distributed observation and control, and possesses the research basis to complete this project.

分布式观测器设计是由多自主体系统和多源信息融合交叉形成的研究课题，为分析和预测复杂系统的运行提供了一类新的研究范式。目前大部分的分布式观测器设计算法都是基于复杂的高维线性矩阵不等式，参数求解过程复杂且有一定的保守性，限制了其在实际工程系统中的应用。本项目旨在通过引入基于采样机制的辅助变量，建立基于多重一致性滤波的分布式观测器框架。通过循序渐进的研究静态网络、动态网络、以及非线性系统三种情形下的分布式观测器设计方案，揭示多重一致性滤波降低参数选取复杂度和保守性的内在机理，发现复杂动态网络对观测器参数及收敛性能的影响，寻找非线性系统全局可检条件的适配方法。分布式观测器参数设计算法和跟踪性能分析过程都会得到简化，为状态信息不完备情形下复杂系统的控制干预奠定重要基础。目前申请人在分布式观测与控制方向已经发表IEEE汇刊长文7篇，ESI高被引论文1篇，具备了完成本项目的研究基础。

为了克服传统的分布式观测器设计算法依赖于求解复杂的线性矩阵不等式这一瓶颈，本项目基于线性变换和代数图论方法，设计了结构简单、参数易于求解的分布式观测器。具体的，针对几类切换网络下的非线性系统的协同编队问题，结合多Lyapunov函数、扩张状态观测器等方法，研究了基于分布式观测器的事件触发控制器设计问题，得到了编队误差有界的充分条件。针对一类分布式观测器的对偶问题，在执行器饱和约束的条件下，基于低增益控制方法，设计了控制器参数，给出了一致性误差半全局收敛的充分条件。最后，将我们的结果拓展应用到航天器交汇对接、多弹协同估计与制导问题中。在本项目的成果支持下，负责人获得2022年中国指挥与控制学会青年科学家奖。