Computing Safe Control Inputs using Discrete-Time Matrix Control Barrier Functions via Convex Optimization
Published in arXiv, 2025
Control barrier functions (CBFs) have seen widespread success in providing forward invariance and safety guarantees for dynamical control systems. The majority of formulations consider continuous-time formulations, but recent focus has shifted to discrete-time dynamics. A crucial limitation of discrete-time formulations is that CBFs that are nonconcave in their argument require the solution of nonconvex optimization problems to compute safety-preserving control inputs, which inhibits real-time computation of control inputs guaranteeing forward invariance. This paper presents a novel method for computing safety-preserving control inputs for discrete-time systems with nonconvex safety sets, utilizing convex optimization and the recently developed class of matrix control barrier function techniques. The efficacy of our methods is demonstrated through numerical simulations on a bicopter system.
Preprint: Link
Recommended citation: J. Usevitch, J. A. Paredes Salazar, and A. Goel, "Computing safe control inputs using discrete-time matrix control barrier functions via convex optimization," arXiv preprint arXiv:2510.09925, submitted to IEEE Trans. Autom. Cont.