arXiv subjects

Elizabeth Dietrich

Publications and source records attributed to Elizabeth Dietrich.

8 recordsLinked to original sources

arXiv2026

Probably Approximately Correct Guarantees for Data-Driven Reachability Analysis: A Theoretical and Empirical Comparison

Reachability analysis evaluates system safety by identifying the set in which states may evolve over a time horizon. Data-driven reachability analysis estimates reachable sets and derives probabilistic guarantees directly from data. Several popular techniques for validating reachable sets---conformal prediction, scenario optimization, and the holdout method---admit similar Probably Approximately Correct (PAC) guarantees. We establish a formal connection between these PAC bounds and present an empirical case study on reachable sets to illustrate the trade-offs associated with these methods. We argue that despite the formal relationship between these techniques, subtle differences arise in both the interpretation of guarantees and the parameterization. We conclude with practical advice on the usage of these methods.

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arXiv2026

Importance Sampling for Statistical Certification of Viable Initial Sets

We study the problem of statistically certifying viable initial sets (VISs)---sets of initial conditions whose trajectories satisfy a given control specification. While VISs can be obtained from model-based methods, these methods typically rely on simplified models. We propose a simulation-based framework to certify VISs by estimating the probability of specification violations under a high-fidelity or black-box model. Since detecting these violations may be challenging due to their scarcity, we propose a sample-efficient framework that leverages importance sampling to target high-risk regions. We derive an empirical Bernstein inequality for weighted random variables, enabling finite-sample guarantees for importance sampling estimators. We demonstrate the proposed approach on two systems and show improved convergence of the resulting bounds on an adaptive cruise control benchmark.

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arXiv2026

Staying on Spec: Real-Time Monitoring under Uncertainty with a Maritime Case Study

Robotic systems must operate under uncertainty while satisfying complex task and safety specifications. Monitoring such specifications under uncertainty remains challenging, as existing formulations typically require extensive data or explicit uncertainty distributions. In this paper, we propose a real-time monitoring framework that reduces data requirements by leveraging data-driven reachable sets for specification evaluation. We instantiate the framework for maritime navigation, where complex specifications arise from traffic rules. We develop a data-efficient pipeline for constructing reachable sets and derive a monitoring formulation suitable for real-time deployment. Simulation and hardware experiments demonstrate robust monitoring under realistic disturbances, achieving improved risk detection compared to state-of-the-art metrics.

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arXiv2026

pacSTL: PAC-Bounded Signal Temporal Logic from Data-Driven Reachability Analysis

Signal Temporal Logic (STL) is an expressive language for specifying behaviors of dynamical systems from continuous signals. However, a limitation of standard STL is its inherently deterministic semantics, which prevents it from accommodating uncertainty. Existing approaches to overcome this limitation are computationally costly and limit real-time capability, requiring repeated trajectory sampling or redesign of probability distributions over atomic propositions whenever the atomic propositions or specifications change. We introduce pacSTL, a framework that combines Probably Approximately Correct (PAC)-bounded reachable set predictions with an interval extension of STL. pacSTL computes lower and upper bounds on atomic robustness values by solving optimization problems over PAC-bounded reachable sets and propagates the bounds through the temporal logic operators. The resulting evaluation yields a PAC-bounded robustness interval at the specification level. We demonstrate the efficiency and relevance of pacSTL by verifying a quadrotor flight scenario and runtime monitoring a maritime navigation encounter.

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arXiv2026

Finite-Step Invariant Sets for Hybrid Systems with Probabilistic Guarantees

Poincare return maps are a fundamental tool for analyzing periodic orbits in hybrid dynamical systems, including legged locomotion, power electronics, and other cyber-physical systems with switching behavior. The Poincare return map captures the evolution of the hybrid system on a guard surface, reducing the stability analysis of a periodic orbit to that of a discrete-time system. While linearization provides local stability information, assessing robustness to disturbances requires identifying invariant sets of the state space under the return dynamics. However, computing such invariant sets is computationally difficult, especially when system dynamics are only available through forward simulation. In this work, we propose an algorithmic framework leveraging sampling-based optimization to compute a finite-step invariant ellipsoid around a nominal periodic orbit using sampled evaluations of the return map. The resulting solution is accompanied by probabilistic guarantees on finite-step invariance satisfying a user-defined accuracy threshold. We demonstrate the approach on two low-dimensional systems and a compass-gait walking model.

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arXiv2025

Data-Driven Reachability with Scenario Optimization and the Holdout Method

Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional systems, recent work has focused on the use of probabilistic methods for computing approximate reachable sets. In this work, we advocate for the use of a general purpose, practical, and sharp method for data-driven reachability: the holdout method. Despite the simplicity of the holdout method, we show -- on several numerical examples including scenario-based reach tubes -- that the resulting probabilistic bounds are substantially sharper and require fewer samples than existing methods for data-driven reachability. Furthermore, we complement our work with a discussion on the necessity of probabilistic reachability bounds. We argue that any method that attempts to de-randomize the bounds, by converting the guarantees to hold deterministically, requires (a) an exponential in state-dimension amount of samples to achieve non-vacuous guarantees, and (b) extra assumptions on the dynamics.

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arXiv2025

Symbolic Control for Autonomous Docking of Marine Surface Vessels

We develop a hierarchical control architecture for autonomous docking maneuvers of a dynamic positioning vessel and provide formal safety guarantees. At the upper-level, we treat the vessel's desired surge, sway, and yaw velocities as control inputs and synthesize a symbolic controller in real-time. The desired velocities are then executed by the vessel's low-level velocity feedback control loop. We next investigate methods to optimize the performance of the proposed control scheme. The results are evaluated on a simulation model of a marine surface vessel in the presence of static obstacles and, for the first time, through physical experiments on a scale model vessel.

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arXiv2025

A beginner guide to Iris, Coq and separation logic

Creating safe concurrent algorithms is challenging and error-prone. For this reason, a formal verification framework is necessary especially when those concurrent algorithms are used in safety-critical systems. The goal of this guide is to provide resources for beginners to get started in their journey of formal verification using the powerful tool Iris. The difference between this guide and many others is that it provides (i) an in-depth explanation of examples and tactics, (ii) an explicit discussion of separation logic, and (iii) a thorough coverage of Iris and Coq. References to other guides and to papers are included throughout to provide readers with resources through which to continue their learning.

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