Interval Estimation for Uncertain Systems via Polynomial Chaos Expansions

This article investigates interval estimation for linear systems with time-invariant probabilistic uncertainty. A two-step interval estimation method, which consists of nominal observer design and estimation error bound analysis, is proposed based on polynomial chaos expansion (PCE) and zonotopic technique. To deal with time-invariant probabilistic uncertainty, the error dynamics is approximated via PCE, which leads to an expanded deterministic linear system. Then intervals of the expanded system and error system are analyzed by zonotopic technique. The interval estimation is achieved by combining nominal observer state and estimated error interval. In a case study, an experimental example and a simulation example show the effectiveness of the proposed method.

Automated summary

This article proposes a two-step interval estimation method for linear systems with time-invariant probabilistic uncertainty, utilizing PCE and zonotopic technique. By approximating error dynamics via PCE and analyzing intervals of the expanded system with zonotopic technique, the interval estimation is achieved by combining nominal observer state and estimated error interval. Experimental and simulation examples in a case study demonstrate the effectiveness of the proposed method.