A Risk-Aware Control: Integrating Worst-Case CVaR with Control Barrier Function

TL;DR

This paper introduces a risk-aware control method that incorporates worst-case CVaR into control barrier functions for nonlinear systems, enhancing safety under stochastic uncertainties with optimization-based solutions.

Contribution

It develops a novel risk-aware control barrier function using worst-case CVaR and provides optimization strategies for different safe set geometries, improving safety guarantees.

Findings

Control inputs for safe sets can be computed via quadratic or semidefinite programs.

The proposed method effectively manages tail risk in safety-critical control.

Numerical examples demonstrate improved safety performance over existing methods.

Abstract

This paper proposes a risk-aware control approach to enforce safety for discrete-time nonlinear systems subject to stochastic uncertainties. We derive some useful results on the worst-case Conditional Value-at-Risk (CVaR) and define a discrete-time risk-aware control barrier function using the worst-case CVaR. On this basis, we present optimization-based control approaches that integrate the worst-case CVaR into the control barrier function, taking into account both safe set and tail risk considerations. In particular, three types of safe sets are discussed in detail: half-space, polytope, and ellipsoid. It is shown that control inputs for the half-space and polytopic safe sets can be obtained via quadratic programs, while control inputs for the ellipsoidal safe set can be computed via a semidefinite program. Through numerical examples of an inverted pendulum, we compare its performance with existing methods and demonstrate the effectiveness of our proposed controller.