Persistently Feasible Robust Safe Control by Safety Index Synthesis and Convex Semi-Infinite Programming

TL;DR

This paper introduces a novel control framework that synthesizes safety indices and employs convex semi-infinite programming to achieve robust, realizable safe control under control limits and bounded uncertainties, reducing conservativeness.

Contribution

It proposes a control-limits aware robust safe control method using safety index synthesis and convex semi-infinite programming, addressing realizability and conservativeness issues in uncertain systems.

Findings

Controller is always realizable under control limits.

Method significantly reduces conservativeness compared to baselines.

Ensures safety under unmodeled uncertainties.

Abstract

Model mismatches prevail in real-world applications. Ensuring safety for systems with uncertain dynamic models is critical. However, existing robust safe controllers may not be realizable when control limits exist. And existing methods use loose over-approximation of uncertainties, leading to conservative safe controls. To address these challenges, we propose a control-limits aware robust safe control framework for bounded state-dependent uncertainties. We propose safety index synthesis to find a robust safe controller guaranteed to be realizable under control limits. And we solve for robust safe control via Convex Semi-Infinite Programming, which is the tightest formulation for convex bounded uncertainties and leads to the least conservative control. In addition, we analyze when and how safety can be preserved under unmodeled uncertainties. Experiment results show that our robust safe controller is always realizable under control limits and is much less conservative than strong baselines.