Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem is non-convex when considering standard Barrier and Density methods for invariant sets, and has been treated heuristically by using auxiliary functions. A convex formulation based on occupation measures is proposed in this paper to solve peak estimation. This method is dual to the auxiliary function approach. Our method will converge to the optimal solution and can recover trajectories even from approximate solutions. This framework is extended to safety analysis by maximizing the minimum of a set of costs along trajectories.

中文翻译：

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使用职业测量的峰值估计和恢复

峰值估计旨在找到动态系统实现的状态函数的最大值。在考虑用于不变集的标准 Barrier 和 Density 方法时，这个问题是非凸的，并且已经通过使用辅助函数进行了启发式处理。本文提出了一种基于占用度量的凸公式来解决峰值估计问题。这种方法对辅助函数方法是双重的。我们的方法将收敛到最优解，甚至可以从近似解中恢复轨迹。通过最大化沿轨迹的一组成本的最小值，该框架被扩展到安全分析。