Related papers: Data-driven Reachability using Christoffel Functio…
Constructing valid confidence sets is a crucial task in statistical inference, yet traditional methods often face challenges when dealing with complex models or limited observed sample sizes. These challenges are frequently encountered in…
We investigate methods to provide safety assurances for autonomous agents that incorporate predictions of other, uncontrolled agents' behavior into their own trajectory planning. Given a learning-based forecasting model that predicts…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…
The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state- a…
The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped…
We provide a new method to approximate a (possibly discontinuous) function using Christoffel-Darboux kernels. Our knowledge about the unknown multivariate function is in terms of finitely many moments of the Young measure supported on the…
Control Barrier Functions (CBFs) have been widely utilized in the design of optimization-based controllers and filters for dynamical systems to ensure forward invariance of a given set of safe states. While CBF-based controllers offer…
We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure…
This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata…
Deploying autonomous systems in safety critical settings necessitates methods to verify their safety properties. This is challenging because real-world systems may be subject to disturbances that affect their performance, but are unknown a…
We develop a novel approach to conformal prediction when the target task has limited data available for training. Conformal prediction identifies a small set of promising output candidates in place of a single prediction, with guarantees…
In this work, we consider how preference models in interactive recommendation systems determine the availability of content and users' opportunities for discovery. We propose an evaluation procedure based on stochastic reachability to…
Random Feature Models (RFMs) have become a powerful tool for approximating multivariate functions and solving partial differential equations efficiently. Sparse Random Feature Expansions (SRFE) improve traditional RFMs by incorporating…
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…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safety-aware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC)…
Constrained reinforcement learning (CRL) has gained significant interest recently, since safety constraints satisfaction is critical for real-world problems. However, existing CRL methods constraining discounted cumulative costs generally…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…