A nonlinear set‐membership filter for on‐line applications

TLDR

The paper develops a guaranteed estimator for general nonlinear systems suitable for online use. The method bounds linearization error, applies a linear set‑membership filter to recursively estimate an ellipsoidal state set under bounded noise and smooth dynamics, and is demonstrated on a two‑state example. The filter achieves a tight linearization‑error bound, provably stable under uniform observability, with error converging to zero when noise is absent and initial error is small, yielding a computationally efficient real‑time estimator. © 2003 John Wiley & Sons, Ltd.

Abstract

Abstract A guaranteed estimator for a general class of nonlinear systems and on‐line usage is developed and analysed. This filter bounds the linearization error, then applies a linear set‐membership filter such that stability guarantees hold for nonlinear systems. A tight bound on the linearization error is found using interval analysis. This filter recursively estimates an ellipsoidal set in which the true state lies. General assumptions include the use of bounded noises and twice continuously differentiable dynamics. When the system is uniformly observable, it is proven that the nonlinear set‐membership filter is stable. In addition, if no noise is present and the initial error is small, the error between the centre of the estimated set and the true value converges to zero. The result is an estimator which is computationally attractive and can be implemented robustly in real‐time. The proposed method is applied to a two‐state example to demonstrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.