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

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