Work

Backup Control Barrier Function Synthesis using Sum-of-Squares Reachability

Year: 2026

Type: preprint

Abstract: Backup control barrier functions (bCBFs) enforce safety for input-constrained nonlinear systems using a pre-certified backup set and controller, but their performance depends strongly on this prescribed pair. This letter develops a constructive method for synthesizing a less conservative backup pair via finite horizon sum-of-squares (SOS) backward reachability. Starting from an initial backup set, we compute an SOS-certified finite horizon backward reachable set and controller that satisfy safety and input constraints while steering trajectories to the original backup set. We then provide conditions under which this certified set becomes a valid backup set for a piecewise backup controller. The resulting backup pair is integrated into the bCBF framework to certify larger safe sets.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.27916

Authors: Chun, Jungbae, Mousavi, Shima Sadat, van Wijk, David E. J., Daş, Ersin, Ames, Aaron D., Biertümpfel, Felix

Institutions: University of Michigan, California Institute of Technology, Illinois Institute of Technology, Auburn University

Topic: Formal Methods in Verification

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Collaborative Research: Robust Control of Large-Scale Networks with Variable Delays using Partial Integral Equations, Collaborative Research: Robust Control of Large-Scale Networks with Variable Delays using Partial Integral Equations

OpenAlex ID: W7204822446

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