期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 67, 期 6, 页码 3021-3028出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2021.3089639
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
资金
- Swedish Research Council (VR)
- Swedish Foundation for Strategic Research (SSF)
- Knut and Alice Wallenberg Foundation (KAW)
- EU CANOPIES project
This article introduces a notion of high-order barrier functions that guarantee set forward invariance by checking their higher order derivatives. A singularity-free control scheme is proposed for controlled dynamical systems, ensuring safety. The article also includes a case study on rigid-body attitude dynamics.
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.
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