Distributed Interval Estimation for Continuous-Time Linear Systems Based on Robust Observer and Interval Analysis
针对连续时间线性系统，提出一种结合鲁棒观测器和区间分析的两步分布式区间估计方法，先通过H∞方法获得点估计，再对误差进行集值分析得到区间估计，并用不一致消除技术提高区间紧致性。
This article aims at investigating distributed interval estimation methods for continuous-time linear time-invariant (LTI) systems. By allying a robust observer design method and interval analysis techniques, we develop a novel two-step interval estimation method for LTI systems whose outputs are measured by a series of nodes connected via a given directed graph. First, a distributed observer formed by a group of local observers is designed via an $H_{\infty } $ approach to obtain an accurate point-valued estimation. This estimation is completed by a reliable interval-valued estimation achieved by a rigorous set-valued analysis of the estimation error dynamics. In order to further enhance the accuracy of the estimated intervals, an elimination by inconsistency technique is applied to characterize the smallest common interval containing the actual state vector of the system. Compared with the existing distributed interval observer approaches, the proposed method can effectively enhance the tightness of the estimated state intervals. Simulation results are shown to support the theoretical findings.