Renato Loureiro | Searcharxiv

arXiv2026

Worst-Case Probability Bounds for Finite-Horizon Safety under Moment Uncertainty

This paper addresses the problem of estimating upper bounds on the probability that a dynamical system will enter an undesirable region at some point within a finite time horizon. The primary source of uncertainty lies in the system's initial state, for which only a finite set of moments is known or within a prescribed interval. To tackle this problem, we formulate a measure-based program and propose its relaxation using the moment-sum-of-squares (moment-SOS) framework. The corresponding dual problem is introduced as a functional program, which is subsequently strengthened into a sum-of-squares (SOS) program. Notably, this dual formulation bears a structural resemblance to classical barrier function techniques for certifying system safety, with the key distinction that it yields a probabilistic certificate. The effectiveness of the proposed approach is demonstrated through multiple case studies, including a case involving an object in orbit.

math.OC↗

arXiv2025

Virtual Target Trajectory Prediction for Stochastic Targets

Trajectory prediction of aerial vehicles is a key requirement in applications ranging from missile guidance to UAV collision avoidance. While most prediction methods assume deterministic target motion, real-world targets often exhibit stochastic behaviors such as evasive maneuvers or random gliding patterns. This paper introduces a probabilistic framework based on Conditional Normalizing Flows (CNFs) to model and predict such stochastic dynamics directly from trajectory data. The learned model generates probability distributions of future target positions conditioned on initial states and dynamic parameters, enabling efficient sampling and exact density evaluation. To provide deterministic surrogates compatible with existing guidance and planning algorithms, sampled trajectories are clustered using a time series k-means approach, yielding a set of representative "virtual target" trajectories. The method is target-agnostic, computationally efficient, and requires only trajectory data for training, making it suitable as a drop-in replacement for deterministic predictors. Simulated scenarios with maneuvering and ballistic targets demonstrate that the proposed approach bridges the gap between deterministic assumptions and stochastic reality, advancing guidance and control algorithms for autonomous vehicles.

cs.RO↗