{"ID":2871967,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.10716","arxiv_id":"2509.10716","title":"Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints","abstract":"This paper investigates the problem of composing multiple control barrier functions (CBFs) -- and matrix control barrier functions (MCBFs) -- through logical and combinatorial operations. Standard CBF formulations naturally enable conjunctive (AND) combinations, but disjunctive (OR) and more general logical structures introduce nonsmoothness and possibly a combinatorial blow-up in the number of logical combinations. We introduce the framework of combinatorial CBFs that addresses p-choose-r safety specifications and their nested composition. The proposed framework ensures safety for the exact safe set in a scalable way, using the original number of primitive constraints. We establish theoretical guarantees on safety under these compositions, and we demonstrate their use on a patrolling problem in a multi-agent system.","short_abstract":"This paper investigates the problem of composing multiple control barrier functions (CBFs) -- and matrix control barrier functions (MCBFs) -- through logical and combinatorial operations. Standard CBF formulations naturally enable conjunctive (AND) combinations, but disjunctive (OR) and more general logical structures...","url_abs":"https://arxiv.org/abs/2509.10716","url_pdf":"https://arxiv.org/pdf/2509.10716v2","authors":"[\"Pio Ong\",\"Haejoon Lee\",\"Tamas G. Molnar\",\"Dimitra Panagou\",\"Aaron D. Ames\"]","published":"2025-09-12T22:13:04Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}