PCA-DDReach: 主成分分析による確率的動的システムの効率的な統計的到達可能性解析
PCA-DDReach: Efficient Statistical Reachability Analysis of Stochastic Dynamical Systems via Principal Component Analysis
ブラックボックスな動的システムの到達可能性解析において、主成分分析を用いて保守性を低減しつつ効率的に確率的到達集合を計算するデータ駆動手法を提案した。
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著者: Navid Hashemi, Lars Lindemann, Jyotirmoy Deshmukh
分類: cs.RO
原文アブストラクト
This study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical systems. However, identifying parametric physical models for complex CPS is challenging due to their complexity, uncertainty, and variability, often rendering them as black-box oracles. As an alternative, one can treat these complex systems as black-box models and use trajectory data sampled from the system (e.g., from high-fidelity simulators or the real system) along with machine learning techniques to learn models that approximate the underlying dynamics. However, these machine learning models can be inaccurate, highlighting the need for statistical tools to quantify errors. Recent advancements in the field include the incorporation of statistical uncertainty quantification tools such as conformal inference (CI) that can provide probabilistic reachable sets with provable guarantees. Recent work has even highlighted the ability of these tools to address the case where the distribution of trajectories sampled during training time are different from the distribution of trajectories encountered during deployment time. However, accounting for such distribution shifts typically results in more conservative guarantees. This is undesirable in practice and motivates us to present techniques that can reduce conservatism. Here, we propose a new approach that reduces conservatism and improves scalability by combining conformal inference with Principal Component Analysis (PCA). We show the effectiveness of our technique on various case studies, including a 12-dimensional quadcopter and a 27-dimensional hybrid system known as the powertrain.
