ArXiv

Optimal Safety Control using High-Order Control Barrier Functions

2026-07-19 · 02:30 UTC ·Neng Li, Zuodong Pan, Jiaxing Wang... ·1 min read
Authors
Neng Li, Zuodong Pan, Jiaxing Wang...
Categories
eess.SY, cs.RO
arXiv
https://arxiv.org/abs/2607.17032v1
PDF
https://arxiv.org/pdf/2607.17032v1

Brief

The paper addresses optimal safety control for nonlinear systems by proposing two novel high-order control barrier functions (HOCBFs) — differing from zeroing HOCBFs — and explicit safety controllers. It develops a high-order control Lyapunov function (HOCLF) using vector Lyapunov methods, proves compatibility with the HOCBFs to enable simultaneous stabilization and safety, and derives an optimal controller; validated on a quadrotor navigation example. Full text was not available (abstract-based summary).

Why it matters

Derives two novel high-order control barrier functions (HOCBFs) — explicitly distinct from zeroing HOCBFs — and provides explicit designs for the resulting safety controllers.

Key details

  • Introduces a high-order control Lyapunov function (HOCLF) via a vector Lyapunov function approach, analyzes compatibility between the HOCLF and HOCBFs to guarantee simultaneous stabilization and safety, and establishes an optimal controller.
  • Validated on a quadrotor navigation numerical example; paper is 8 pages with 3 figures, accepted by ASCC2026 and posted as arXiv:2607.17032v1 (published 2026-07-19).
Source evidence

Abstract

This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.

Comment: 8 pages, 3 figures, Accepted by ASCC2026