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arXiv · 2506.10296

Synthesizing Min-Max Control Barrier Functions For Switched Affine Systems

Sara Kamali·Guillaume O. Berger·Sriram Sankaranarayanan
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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.

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Sara Kamali, Guillaume O. Berger, Sriram Sankaranarayanan. 2025-06-12. Synthesizing Min-Max Control Barrier Functions For Switched Affine Systems. https://arxiv.org/abs/2506.10296

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