A Semialgebraic Framework for Verification and Synthesis of Control Barrier Functions

• 成果类型: Article
• 署名作者: Clark, Andrew
• 署名单位: Washington University (WUSTL)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3497001
• 发表日期: 2025
• 关键词: QUADRATIC PROGRAMS

摘要

Safety is a critical property for control systems in medicine, transportation, manufacturing, and other applications, and can be defined as ensuring positive invariance of a predefined safe set. This article investigates the problems of verifying positive invariance of a semialgebraic set as well as synthesizing sets that can be made positive invariant through control barrier function (CBF)-based control. The key to our approach consists of mapping conditions for positive invariance to sum-of-squares constraints via the Positivstellensatz from real algebraic geometry. Based on these conditions, we propose a framework for verifying safety of CBF-based control including single CBFs, high-order CBFs, multi-CBFs, and systems with trigonometric dynamics and actuation constraints. In the area of synthesis, we propose algorithms for constructing CBFs, namely, an alternating-descent approach and a local CBF approach. We evaluate our approach through case studies on quadrotor UAV and power converter test systems.