62 / 2025-03-29 23:14:08

Boundary Analysis of the Zonotopic State Estimation Based on Uncertainty Measure

interval estimation, uncertainty theory, zonotopes, linear discrete systems

The set-based interval estimation method generates rigorously reliable intervals. While demonstrating high accuracy, this approach tends to produce estimation results with limited tightness. Nevertheless, in practical dynamical systems, quantitative measures of uncertainty are frequently obtainable. This paper presents a methodological framework for analyzing zonotopic boundaries by incorporating uncertainty measures. Specifically, a formal definition of zonotopes under uncertainty measures is established, and the uncertainty measures of the linear operations of zonotopes are derived. Furthermore,  the boundaries of the states with different uncertain measures are derived, which realize the boundary analysis of the zonotopic state estimation. The efficacy of the proposed method is validated through numerical simulations.