Convex Co-Design of Control Barrier Functions and State Feedback Controllers for Linear Systems With Input Constraints

• 成果类型: Article
• 署名作者: Wang, Han; Margellos, Kostas; Papachristodoulou, Antonis; De Persis, Claudio
• 署名单位: University of Oxford; University of Groningen
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3638061
• 发表日期: 2026
• 关键词: SET INVARIANCE

摘要

In this article, we study the problem of co-designing control barrier functions (CBFs) and affine state feedback controllers for continuous-time linear systems. The co-design problem is known to be generally nonconvex due to the multiplicative coupling between the CBF and the controller required for control invariance. To address this challenge, we propose a convex reformulation based on an appropriate parameterization of the CBF and the controller for different problem settings and solve a single semidefinite program to co-design the CBF and the controller. Since our method does not exploit the relative degree of the system with respect to the safe set, it neither incur issues with high- and mixed-relative degree nor does it rely on backstepping to design barrier functions and controllers. We also show that 2-norm and polytopic bounds on the constrained input can be incorporated as convex constraints into the co-design program. We demonstrate the effectiveness of our approach using numerical examples involving high- and mixed-relative degree systems.