发表机构
Clemson University（克莱姆森大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出数据到证书（D2C）范式，直接学习Koopman超特征函数作为不等式证书，用于稳定性、安全性和控制，并通过几何与预解式方法实现数据驱动认证。
AI 中文摘要
传统动力系统模型，包括Koopman算子表示，从根本上基于等式，而许多分析和控制工具依赖于不等式。这种不匹配促使人们寻求与分析及控制综合问题中的认证任务内在对齐的表示。在本文中，我们提出了一种“数据到证书（D2C）”范式，绕过显式模型构建，直接从数据中学习证书。我们引入了Koopman算子的超特征函数，作为特征函数基于不等式的一般化，定义编码稳定性、安全性和不确定性传播的指数增长包络，从而为一系列控制目标提供证书。我们建立了其理论基础，并表明相关速率可恢复内在动力学量，如Lyapunov指数。我们开发了两种互补的构造方法：一种基于乘法遍历定理（MET）的几何方法，以及一种可直接从轨迹数据计算的预解式/Gramian公式。由此产生的框架提供了可用于稳定性和收缩分析以及通过基于凸二次规划的优化程序进行稳定和安全关键控制综合的证书。数值示例证明了所提出的数据驱动认证方法在稳定化、收缩和安全控制设计中的有效性。
英文摘要
Traditional dynamical system models, including Koopman operator representations, are fundamentally equality-based, whereas many analysis and control tools rely on inequalities. This mismatch motivates representations that are intrinsically aligned with certification tasks involved in the analysis and control synthesis problems. In this paper, we propose a \emph{data-to-certificates (D2C)} paradigm that bypasses explicit model construction and directly learns certificates from data. We introduce \emph{supereigenfunctions} of the Koopman operator as an inequality-based generalization of eigenfunctions that define exponential growth envelopes encoding stability, safety, and uncertainty propagation, thereby serving as certificates for a range of control objectives. We establish their theoretical foundations and show that the associated rates recover intrinsic dynamical quantities such as Lyapunov exponents. Two complementary constructions are developed: a geometric approach based on the multiplicative ergodic theorem (MET), and a resolvent/Gramian formulation that enables computation directly from trajectory data. The resulting framework yields certificates that can be used for stability and contraction analysis, as well as stabilizing and safety-critical control synthesis via convex quadratic programming-based optimization program. Numerical examples demonstrate the effectiveness of the proposed data-driven certification approach for stabilization, contraction, and safe control design.
