Sufficient Conditions for Uniform Asymptotic Stability and Input-to-State Stability Using High-Order Control Barrier Functions

• 成果类型: Article
• 署名作者: Marley, Mathias; Skjetne, Roger; Teel, Andrew R.
• 署名单位: Norwegian University of Science & Technology (NTNU); University of California System; University of California Santa Barbara
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3332018
• 发表日期: 2024
• 页码: 2352-2366
• 关键词: Control barrier functions (CBFs); input-to-state stability; uniform asymptotic stability

摘要

Control barrier functions (CBFs) ensure the safety of controlled dynamical systems by enforcing forward invariance of safe subsets of the state space. First-order CBFs are applicable for systems where the control input appears in the first time derivative of the controlled output. High-order CBFs (HOCBFs) extend the notion of CBFs to systems of any order, following a procedure reminiscent of the recursive design of a control Lyapunov function in backstepping. Asymptotic stability of compact safe sets for Lipschitz continuous HOCBF-based controllers has recently been reported in the literature. In this article, we extend this result by establishing sufficient conditions for uniform asymptotic stability of closed, but not necessarily compact, safe sets. Moreover, we show that uniform asymptotic stability holds for differential inclusions that correspond to allowing the control input to take on arbitrary values that satisfy the HOCBF-induced input constraints. This result circumvents the need to establish continuity properties of optimization-based safeguarding control laws. Sufficient conditions for input-to-state stability are also established, by constructing a vector comparison system from the worst case evolution of the HOCBF along the disturbed versions of the aforementioned differential inclusions. The theoretical results are illustrated by two case studies.