提出分层优化框架，让安全约束优先于其他目标，避免传统方法因参数不当导致失效。
Safety-critical Control with Control Barrier Functions: A Hierarchical Optimization Framework
- 将多目标优化拆解为嵌套子问题，安全优先逐步求解
- 在保证安全的前提下提升可行性与收敛速度，避免传统方法的无解问题
- 适用于多个安全约束场景，适合高可靠性系统设计者
控制屏障函数（CBF）自问世以来已成为安全关键系统设计的基础工具。通常采用二次规划（QP）框架来整合CBF、控制李雅普诺夫函数（CLF）、其他约束及名义控制设计。然而，该约束优化框架涉及需权衡不同目标与约束的超参数，若未预先合理调优，会影响系统性能甚至导致不可行。本文提出一种分层优化框架，将多目标优化问题以安全优先的方式分解为嵌套的子问题。新框架在确保安全的前提下最大化性能与可行性，并可轻松扩展至多证书情形。通过直观可视化分析，系统对比了所提方法与现有基于QP方法在安全性、可行性与收敛速率上的优势。此外，两个数值例子验证了分析结果，展示了所提方法的优越性。
原文摘要 · Abstract (English)
The control barrier function (CBF) has become a fundamental tool in safety-critical systems design since its invention. Typically, the quadratic optimization framework is employed to accommodate CBFs, control Lyapunov functions (CLFs), other constraints and nominal control design. However, the constrained optimization framework involves hyper-parameters to tradeoff different objectives and constraints, which, if not well-tuned beforehand, impact system performance and even lead to infeasibility. In this paper, we propose a hierarchical optimization framework that decomposes the multi-objective optimization problem into nested optimization sub-problems in a safety-first approach. The new framework addresses potential infeasibility on the premise of ensuring safety and performance as much as possible and applies easily in multi-certificate cases. With vivid visualization aids, we systematically analyze the advantages of our proposed method over existing QP-based ones in terms of safety, feasibility and convergence rates. Moreover, two numerical examples are provided that verify our analysis and show the superiority of our proposed method.
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