Temporal Logic Control for Nonlinear Stochastic Systems Under Unknown Disturbances

TL;DR

This paper introduces a data-driven, abstraction-based framework for synthesizing robust control strategies for nonlinear stochastic systems under unknown disturbances, ensuring compliance with temporal logic specifications.

Contribution

It develops a novel UMDP abstraction method that tightly bounds uncertainties and improves control synthesis efficiency for complex systems with unknown disturbances.

Findings

Tighter uncertainty bounds via convex polytopes.

Enhanced control synthesis performance over existing methods.

Validated effectiveness through multiple case studies.

Abstract

In this paper, we present a novel framework to synthesize robust strategies for discrete-time nonlinear systems with random disturbances that are unknown, against temporal logic specifications. The proposed framework is data-driven and abstraction-based: leveraging observations of the system, our approach learns a high-confidence abstraction of the system in the form of an uncertain Markov decision process (UMDP). The uncertainty in the resulting UMDP is used to formally account for both the error in abstracting the system and for the uncertainty coming from the data. Critically, we show that for any given state-action pair in the resulting UMDP, the uncertainty in the transition probabilities can be represented as a convex polytope obtained by a two-layer state discretization and concentration inequalities. This allows us to obtain tighter uncertainty estimates compared to existing approaches, and guarantees efficiency, as we tailor a synthesis algorithm exploiting the structure of this UMDP. We empirically validate our approach on several case studies, showing substantially improved performance compared to the state-of-the-art.