Divide and Discard: Fast Tightening of Guaranteed State Bounds for Nonlinear Systems

TL;DR

The paper introduces a divide-and-discard method for guaranteed state estimation in nonlinear systems, which refines state bounds efficiently by discarding many sets early, leading to faster and tighter estimations.

Contribution

It presents a simple, scalable divide-and-discard approach that improves computational efficiency and enclosure tightness over existing guaranteed observers.

Findings

Outperforms state-of-the-art methods in efficiency and tightness.

Computational complexity scales quadratically with state dimension.

Effective in nonlinear benchmark problems.

Abstract

We propose a simple yet effective divide-and-discard (DD) approach to guaranteed state estimation for nonlinear discrete-time systems. Our method iteratively subdivides interval enclosures of the state and propagates them forward in time using a mean-value enclosure. The central idea is to rely on repeated refinement of simple sets rather than on more complex set representations, yielding an observer that is straightforward to implement and easy to integrate into existing frameworks. Our divide-and-discard strategy exploits that many sets can be discarded early and limits the number of maintained sets, resulting in low computational cost with complexity that scales only quadratically in the state dimension. The proposed method is evaluated on nonlinear benchmark problems previously used to compare guaranteed observers, where it outperforms state-of-the-art approaches in terms of both computational efficiency and enclosure tightness.