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.