From Time-Invariant to Uniformly Time-Varying Control Barrier Functions: A Constructive Approach
<|reference_start|>From Time-Invariant to Uniformly Time-Varying Control Barrier Functions: A Constructive Approach: In this paper, we define and analyze a subclass of (time-invariant) Control Barrier Functions (CBF) that have favorable properties for the construction of uniformly timevarying CBFs and thereby for the satisfaction of uniformly time-varying constraints. We call them {\Lambda}-shiftable CBFs where {\Lambda} states the extent by which the CBF can be varied by adding a time-varying function. Moreover, we derive sufficient conditions under which a time-varying CBF can be obtained from a time-invariant one, and we propose a systematic construction method. Advantageous about our approach is that a {\Lambda}-shiftable CBF, once constructed, can be reused for various control objectives. In the end, we relate the class of {\Lambda}-shiftable CBFs to Control Lyapunov Functions (CLF), and we illustrate the application of our results with a relevant simulation example.<|reference_end|>
@article{wiltz2024from,
    title={From Time-Invariant to Uniformly Time-Varying Control Barrier Functions:
  A Constructive Approach},
    author={Adrian Wiltz, Dimos V. Dimarogonas},
    journal={arXiv preprint arXiv:2408.12964},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.12964},
    primaryClass={eess.SY cs.SY}
}