Fast Verification of Control Barrier Functions via Linear Programming

TL;DR

This paper introduces a linear programming-based method for efficiently verifying control barrier functions, significantly reducing computational time compared to traditional semidefinite programming approaches, thus enhancing system safety verification.

Contribution

It presents a novel linear programming approach for verifying control barrier functions, replacing semidefinite programming to improve scalability and efficiency.

Findings

Verification time reduced by over 95% in simulations

Method applicable to multiple candidate functions simultaneously

Scales better than traditional semidefinite programming methods

Abstract

Control barrier functions are a popular method of ensuring system safety, and these functions can be used to enforce invariance of a set under the dynamics of a system. A control barrier function must have certain properties, and one must both formulate a candidate control barrier function and verify that it does indeed satisfy the required properties. Targeting the latter problem, this paper presents a method of verifying any finite number of candidate control barrier functions with linear programming. We first apply techniques from real algebraic geometry to formulate verification problem statements that are solvable numerically. Typically, semidefinite programming is used to verify candidate control barrier functions, but this does not always scale well. Therefore, we next apply a method of inner-approximating the set of sums of squares polynomials that significantly reduces the computational complexity of these verification problems by transcribing them to linear programs. We give explicit forms for the resulting linear programs, and simulation results for a satellite inspection problem show that the computation time needed for verification can be reduced by more than 95%.