Data-Driven Reachability Analysis from Noisy Data

Abstract

We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing over-approximated reachable sets based on matrix zonotopes is proposed for linear systems. Constrained matrix zonotopes are introduced to provide less conservative reachable sets at the cost of increased computational expenses and utilized to incorporate prior knowledge about the unknown system model. Then we extend the approach to polynomial systems and, under the assumption of Lipschitz continuity, to nonlinear systems. Theoretical guarantees are given for these algorithms in that they give a proper over-approximate reachable set containing the true reachable set. Multiple numerical examples and real experiments show the applicability of the introduced algorithms, and comparisons are made between algorithms.

This paper is accepted at the IEEE Transactions on Automatic Control

References in corpus (2)

• Combining Prior Knowledge and Data for Robust Controller Design
• Sampling-based Reachability Analysis: A Random Set Theory Approach with Adversarial Sampling

Cited by in corpus (4)

• Robust Data-Driven Tube-Based Zonotopic Predictive Control with Closed-Loop Guarantees
• Sampling-based Stochastic Data-driven Predictive Control under Data Uncertainty - Extended Version
• Data-driven Reachability using Christoffel Functions and Conformal Prediction
• Stochastic Data-driven Predictive Control of Linear Systems with Sub-Gaussian Disturbances using Causal Predictors