Feasibility and Regularity Analysis of Safe Stabilizing Controllers under Uncertainty

TL;DR

This paper investigates the conditions under which safe stabilizing controllers can be feasibly designed for uncertain control-affine systems using control barrier functions and second-order cone constraints.

Contribution

It introduces a framework for analyzing the feasibility and regularity of controllers that ensure safety and stability under uncertainty using SOCCs.

Findings

Feasibility conditions for SOCCs in uncertain systems

Regularity properties of controllers satisfying safety constraints

Framework applicable to probabilistic and worst-case error descriptions

Abstract

This paper studies the problem of safe stabilization of control-affine systems under uncertainty. Our starting point is the availability of worst-case or probabilistic error descriptions for the dynamics and a control barrier function (CBF). These descriptions give rise to second-order cone constraints (SOCCs) whose simultaneous satisfaction guarantees safe stabilization. We study the feasibility of such SOCCs and the regularity properties of various controllers satisfying them.