High-Order Barrier Functions: Robustness, Safety, and Performance-Critical Control

• 成果类型: Article
• 署名作者: Tan, Xiao; Shaw Cortez, Wenceslao; Dimarogonas, Dimos V.
• 署名单位: Royal Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3089639
• 发表日期: 2022
• 页码: 3021-3028
• 关键词: safety; Robustness; asymptotic stability; control systems; tools; Perturbation methods; Lyapunov methods; Control barrier functions; high-order systems; set asymptotic stability; set invariance

摘要

In this article, we propose a notion of high-order (zeroing) barrier functions (HOBFs) that generalizes the concept of zeroing barrier functions and guarantees set forward invariance by checking their higher order derivatives. The proposed formulation guarantees asymptotic stability of the forward invariant set, which is highly favorable for robustness with respect to model perturbations. No forward completeness assumption is needed in our setting in contrast to existing HOBF methods. For the case of controlled dynamical systems, we relax the requirement of uniform relative degree and propose a singularity-free control scheme that yields a locally Lipschitz control signal and guarantees safety. Furthermore, the proposed formulation accounts for performance-critical control: it guarantees that a subset of the forward invariant set will admit any existing, bounded control law while still ensuring forward invariance of the set. Finally, a nontrivial case study with rigid-body attitude dynamics and interconnected cell regions as the safe region is investigated.