一句话：综述区间与集合方法在控制与状态估计中的离线分析与在线实现，并回顾多类实际应用。
控制与状态估计需要应对参数不精确、初始条件不确定和外部扰动。区间方法及其他集合值技术可用于动态系统模型的参数辨识，并对控制器与状态估计器进行可验证的可行性和稳定性分析。这些方法传统上多用于离线分析由经典浮点过程设计的系统模型；近年来，区间与集合方法也被发展为可直接求解相关设计任务，并实现在线可靠技术，包括集合式模型预测控制、非线性变结构控制与反步控制中的在线参数自适应、区间观测器以及故障诊断。本文梳理其方法论背景，并回顾大量已成功应用这些方法的实际案例。
Control and state estimation procedures need to be robust against imprecisely known parameters, uncertainty in initial conditions, and external disturbances. Interval methods and other set-based techniques form the basis for the implementation of powerful approaches that can be used to identify parameters of dynamic system models in the presence of the aforementioned types of uncertainty. Moreover, they are applicable to a verified feasibility and stability analysis of controllers and state estimators. In addition to these approaches which are typically used offline for analysis of system models designed with classical floating point procedures, interval and set-based methods have also been developed in recent years, which allow to directly solve the associated design tasks and to implement reliable techniques that are applicable online, i.e., during system operation. The latter approaches include set-based model predictive control, online parameter adaptation techniques for nonlinear variable-structure and backstepping controllers, interval observers, and fault diagnosis techniques. This paper provides an overview of the methodological background and reviews numerous practical applications for which interval and other set-valued approaches have been employed successfully.
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@article{RauhLRJDRF25,
title = {Offline and Online Use of Interval and Set-Based Approaches for Control and State Estimation: A Selection of Methodological Approaches and Their Application},
author = {Andreas Rauh and Marit Lahme and Simon Rohou and Luc Jaulin and Thach Ngoc Dinh and Tarek Raissi and Mohamed Fnadi},
journal = {Logical Methods in Computer Science},
volume = {Volume 21, Issue 4},
year = {2025},
doi = {10.46298/lmcs-21(4:11)2025}
}