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Main Authors: Kamali, Sara, Berger, Guillaume O., Sankaranarayanan, Sriram
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.10296
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author Kamali, Sara
Berger, Guillaume O.
Sankaranarayanan, Sriram
author_facet Kamali, Sara
Berger, Guillaume O.
Sankaranarayanan, Sriram
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_10296
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Synthesizing Min-Max Control Barrier Functions For Switched Affine Systems
Kamali, Sara
Berger, Guillaume O.
Sankaranarayanan, Sriram
Systems and Control
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.
title Synthesizing Min-Max Control Barrier Functions For Switched Affine Systems
topic Systems and Control
url https://arxiv.org/abs/2506.10296