Synthesizing Min-Max Control Barrier Functions For Switched Affine Systems

TL;DR

This paper develops a method to synthesize non-smooth control barrier functions for switched affine systems, enabling safety guarantees through a systematic, automated approach using nonsmooth analysis and combinatorial optimization techniques.

Contribution

It introduces a novel framework for synthesizing min- and max-affine control barrier functions for switched affine systems, including a tree-search algorithm for automation.

Findings

Successfully applied to several switched affine system examples.

Automated synthesis of CBFs enhances safety guarantees.

Framework leverages nonsmooth analysis for non-smooth CBFs.

Abstract

We study the problem of synthesizing non-smooth control barrier functions (CBFs) for continuous-time switched affine systems. Switched affine systems are defined by a set of affine dynamical modes, wherein the control consists of a state-based switching signal that determines the current operating mode. The control barrier functions seek to maintain the system state inside a control invariant set that excludes a given set of unsafe states. We consider CBFs that take the form of pointwise minima and maxima over a finite set of affine functions. Our approach uses ideas from nonsmooth analysis to formulate conditions for min- and max- affine control barrier functions. We show how a feedback switching law can be extracted from a given CBF. Next, we show how to automate the process of synthesizing CBFs given a system description through a tree-search algorithm inspired by branch-and-cut methods from combinatorial optimization. Finally, we demonstrate our approach on a series of interesting examples of switched affine systems.