We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented as a semidefinite program that can be solved numerically. Furthermore, the method is agnostic of whether data is generated through a deterministic or stochastic process, so its implementation requires no prior adjustments by the user to accommodate these different scenarios. Rigorous convergence results justify the applicability of the method, while also extending and uniting similar results from across the literature. Examples on discovering Lyapunov functions, performing ergodic optimization, and bounding extrema over attractors for both deterministic and stochastic dynamics exemplify these convergence results and demonstrate the performance of the method.

翻译：我们提出了一种灵活的数据驱动动力系统分析方法，该方法无需显式的模型发现。该方法根植于从数据中近似库普曼算子的成熟技术，并实现为可数值求解的半定规划。此外，该方法对数据是通过确定性过程还是随机过程生成无偏好，因此在实际应用时无需用户预先调整以适应不同场景。严格的收敛结果验证了该方法的适用性，同时扩展并统一了文献中的相关结论。通过发现李雅普诺夫函数、进行遍历优化以及约束确定性及随机动力学吸引子极值的实例，这些收敛结果得以具体体现，并展示了该方法的性能。