区分確率バリア関数
Piecewise Stochastic Barrier Functions
確率システムの安全性解析のための区分関数ベースの確率バリア関数フレームワークを提案し、区分定数バリア関数の合成をミニマックス最適化問題に帰着させ、効率的な3つのアルゴリズムを導入した。
著者: Rayan Mazouz, Frederik Baymler Mathiesen, Luca Laurenti, Morteza Lahijanian
分類: cs.RO
原文アブストラクト
This paper presents a novel stochastic barrier function (SBF) framework for safety analysis of stochastic systems based on piecewise (PW) functions. We first outline a general formulation of PW-SBFs. Then, we focus on PW-Constant (PWC) SBFs and show how their simplicity yields computational advantages for general stochastic systems. Specifically, we prove that synthesis of PWC-SBFs reduces to a minimax optimization problem. Then, we introduce three efficient algorithms to solve this problem, each offering distinct advantages and disadvantages. The first algorithm is based on dual linear programming (LP), which provides an exact solution to the minimax optimization problem. The second is a more scalable algorithm based on iterative counter-example guided synthesis, which involves solving two smaller LPs. The third algorithm solves the minimax problem using gradient descent, which admits even better scalability. We provide an extensive evaluation of these methods on various case studies, including neural network dynamic models, nonlinear switched systems, and high-dimensional linear systems. Our benchmarks demonstrate that PWC-SBFs outperform state-of-the-art methods, namely sum-of-squares and neural barrier functions, and can scale to eight dimensional systems.
