Optimal Safety Control using High-Order Control Barrier Functions

2026-07-18

AI Summary

This work addresses the problem of optimal safe control for nonlinear systems by proposing two novel classes of higher-order control barrier functions (HOCBFs) and a higher-order control Lyapunov function (HOCLF) constructed via the vector Lyapunov method. These constructs enable the explicit design of controllers that simultaneously satisfy stability and safety constraints. By establishing a synergistic mechanism between HOCBFs and HOCLF within an optimal control framework, the approach achieves a unified and compatible realization of safety and stability objectives. Theoretical analysis clarifies the relationship and advancements of the proposed method relative to existing approaches, while experimental validation on a quadrotor navigation task demonstrates its effectiveness in ensuring both system safety and stability.

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.

Problem

• safety control
• nonlinear control systems
• stabilization
• optimal control
• control barrier functions

Innovation

• High-Order Control Barrier Functions
• Control Lyapunov Functions
• Safety Control
• Nonlinear Control Systems
• Optimal Control