Peak Estimation and Recovery with Occupation Measures

TL;DR

This paper introduces a convex occupation measure-based framework for peak estimation in dynamical systems, providing convergence guarantees and trajectory recovery, and extends it to safety analysis by optimizing cost functions.

Contribution

It presents a novel convex formulation for peak estimation using occupation measures, which converges to the optimal solution and enables trajectory recovery from approximate solutions.

Findings

The method converges to the true peak value.

It can recover system trajectories from approximate solutions.

Extended to safety analysis by optimizing minimum costs.

Abstract

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.