Title: Probabilistic Region-of-Attraction Estimation with Scenario Optimization and Converse Theorems Show Chinese title

Title: 基于情景优化和逆定理的概率吸引域估计

Abstract: The region of attraction characterizes well-behaved and safe operation of a nonlinear system and is hence sought after for verification. In this paper, a framework for probabilistic region of attraction estimation is developed that combines scenario optimization and converse theorems. With this approach, the probability of an unstable condition being included in the estimate is independent of the system's complexity, while convergence in probability to the true region of attraction is proven. Numerical examples demonstrate the effectiveness for optimization-based control applications. Combining systems theory and sampling, the complexity of Monte--Carlo-based verification techniques can be reduced. The results can be extended to arbitrary level sets of which the defining function can be sampled, such as finite-horizon viability. Thus, the proposed approach is applicable and/or adaptable to verification of a wide range of safety-related properties for nonlinear systems including feedback laws based on optimization or learning. Show Chinese abstract

Abstract: 吸引域很好地表征了非线性系统的良好和安全操作，因此被广泛用于验证。 本文开发了一种基于情景优化和逆定理的吸引域概率估计框架。 通过这种方法，不稳定条件被包含在估计中的概率与系统的复杂性无关，同时证明了以概率收敛到真实的吸引域。 数值例子展示了该方法在基于优化的控制应用中的有效性。 结合系统理论和采样技术，蒙特卡洛验证技术的复杂度可以降低。 结果可以扩展到任意的水平集，这些水平集的定义函数可以采样，例如有限时间可行域。 因此，所提出的方法适用于验证广泛的非线性系统的安全性相关属性，包括基于优化或学习的反馈律。