Fine-Tuned Convex Approximations of Probabilistic Reachable Sets under Data-driven Uncertainties

Pengchen Wu, Sonia Martínez and Jun Chen
IEEE Transactions on Automation Science and Engineering, under review

Abstract:

This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded reachable set of the system. Instead, we turn to find a PRS that bounds system states with high confidence. Our data-driven approach builds on a kernel density estimator (KDE) accelerated by a fast Fourier transform (FFT), which is customized to model the uncertainties and obtain the PRS efficiently. However, the non-convex shape of the PRS can make it impractical for subsequent optimal designs. Motivated by this, we formulate a mixed integer nonlinear programming (MINLP) problem whose solution result is an optimal n sided convex polygon that approximates the PRS. Leveraging this formulation, we propose a heuristic algorithm to find this convex set efficiently while ensuring accuracy. The algorithm is tested on comprehensive case studies that demonstrate its near-optimality, accuracy, efficiency, and robustness. The benefits of this work pave the way for promising applications to safety-critical, real-time motion planning of uncertain dynamic systems.

File: (main.pdf)

Bib-tex entry:

@article{PW-SM-JC:23-tase,
author = {P. Wu and S. Mart{\'\i}nez and J. Chen},
title = {Fine-Tuned Convex Approximations of Probabilistic Reachable Sets under Data-driven Uncertainties},
journal= {IEEE Transactions on Automation Science and Engineering},
pages = {},
volume = {},
number = {},
year = {2023},
note = {Under review}
}