{"ID":2874643,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.04220","arxiv_id":"2509.04220","title":"Compatibility of Multiple Control Barrier Functions for Constrained Nonlinear Systems","abstract":"Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to synthesize provably safe controllers that handle multiple state constraints. This paper presents a framework for constrained control of nonlinear systems subject to box constraints on the systems' vector-valued outputs using multiple CBFs. Our results illustrate that when the output has a vector relative degree, the CBF constraints encoding these box constraints are compatible, and the resulting optimization-based controller is locally Lipschitz continuous and admits a closed-form expression. Additional results are presented to characterize the degradation of nominal tracking objectives in the presence of safety constraints. Simulations of a planar quadrotor are presented to demonstrate the efficacy of the proposed framework.","short_abstract":"Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to synthesize provably safe controllers that handle multiple state constraints. This paper...","url_abs":"https://arxiv.org/abs/2509.04220","url_pdf":"https://arxiv.org/pdf/2509.04220v1","authors":"[\"Max H. Cohen\",\"Eugene Lavretsky\",\"Aaron D. Ames\"]","published":"2025-09-04T13:52:11Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"cs.RO\",\"math.OC\"]","methods":"[]","has_code":false}