Peak Estimation for Uncertain and Switched Systems

TL;DR

This paper extends peak estimation methods to uncertain and switched systems using optimal control and occupation measures, enabling bounds on extreme values despite uncertainties and switching behaviors.

Contribution

It introduces a novel framework combining optimal control and occupation measures to handle uncertainty and switching in peak estimation problems.

Findings

Framework effectively bounds extreme values in uncertain systems.

Method accommodates time-dependent and switching uncertainties.

Solution approach uses Linear Matrix Inequalities from moment-SOS hierarchy.

Abstract

Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty. Techniques from optimal control are used to incorporate uncertainty into an existing occupation measure-based peak estimation framework, which includes special consideration for handling switching uncertainties. The resulting infinite-dimensional linear programs can be solved approximately with Linear Matrix Inequalities arising from the moment-SOS hierarchy.