Data-Driven Set-Based Estimation using Matrix Zonotopes with Set Containment Guarantees.

TL;DR: In this paper, a data-driven set propagation function is proposed to estimate the state of an unknown dynamical system with set-containment guarantees, making it applicable to the estimation of safety-critical systems.

Abstract: We propose a method to perform set-based state estimation of an unknown dynamical system using a data-driven set propagation function. Our method comes with set-containment guarantees, making it applicable to the estimation of safety-critical systems. The method consists of two phases: (1) an offline learning phase where we collect noisy state-input data to determine a function to propagate the state-set ahead in time; and (2) an online estimation phase consisting of a time update and a measurement update. It is assumed that sets bound measurement noise and disturbances, but we assume no knowledge of their statistical properties. These sets are described using zonotopes, allowing efficient propagation and intersection operations. We propose two approaches to perform the measurement update. The method is extended to constrained zonotopes. Simulations show that the proposed estimator yields state sets comparable in volume to the confidence bounds obtained by a Kalman filter approach, but with the addition of state set-containment guarantees. We observe that using constrained zonotopes yields smaller sets, but with higher computational cost compared to unconstrained zonotopes.