线性描述系统的极小极大状态估计
Minimax state estimation for linear descriptor systems
AI总结：
针对具有未知但有界模型误差和随机观测噪声的线性微分代数方程，基于广义卡尔曼对偶原理，提出了极小极大状态估计理论与算法。
摘要：
作者对候选科学（物理与数学）学位论文的总结。该论文旨在开发适用于线性无界非可逆算子的广义卡尔曼对偶概念，并引入线性微分代数方程的极小极大状态估计理论与算法。具体而言，论文追求以下目标：- 为具有未知但有界模型误差和随机观测噪声（其相关算子未知但有界）的DAE开发极小极大状态估计理论的广义对偶概念；- 推导具有未知但有界模型误差和随机观测噪声（其相关算子未知但有界）的线性DAE的极小极大状态估计理论；- 描述DAE模型如何传播不确定参数；- 估计最坏情况误差；- 构建滤波器形式的快速估计算法；- 开发模型验证工具，即评估模型对观测现象的描述程度。 论文包含以下新结果：- 提出了卡尔曼对偶原理的广义版本，允许处理具有非平凡零空间的线性无界模型算子；- 基于广义卡尔曼对偶原理，提出了DAE的极小极大估计的新定义；- 证明了极小极大估计的存在性定理；- 提出了DAE的新的极小极大状态估计算法（滤波器形式和变分形式）。
英文摘要：
Author's Summary of the dissertation for the degree of the Candidate of Science (physics and mathematics). The aim of the dissertation is to develop a generalized Kalman Duality concept applicable for linear unbounded non-invertible operators and introduce the minimax state estimation theory and algorithms for linear differential-algebraic equations. In particular, the dissertation pursues the following goals: - develop generalized duality concept for the minimax state estimation theory for DAEs with unknown but bounded model error and random observation noise with unknown but bounded correlation operator; - derive the minimax state estimation theory for linear DAEs with unknown but bounded model error and random observation noise with unknown but bounded correlation operator; - describe how the DAE model propagates uncertain parameters; - estimate the worst-case error; - construct fast estimation algorithms in the form of filters; - develop a tool for model validation, that is to assess how good the model describes observed phenomena. The dissertation contains the following new results: - generalized version of the Kalman duality principle is proposed allowing to handle unbounded linear model operators with non-trivial null-space; - new definitions of the minimax estimates for DAEs based on the generalized Kalman duality principle are proposed; - theorems of existence for minimax estimates are proved; - new minimax state estimation algorithms (in the form of filter and in the variational form) for DAE are proposed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
