Multi-Rate Control Design Under Input Constraints via Fixed-Time Barrier Functions.

Abstract

In this letter, we introduce the notion of periodic safety, which requires that the system trajectories periodically visit a subset of a forward-invariant safe set, and utilize it in a multi-rate framework where a high-level planner generates a reference trajectory that is tracked by a low-level controller under input constraints. We introduce the notion of fixed-time barrier functions which is leveraged by the proposed low-level controller in a quadratic programming framework. Then, we design a model predictive control policy for high-level planning with a bound on the rate of change for the reference trajectory to guarantee that periodic safety is achieved. We demonstrate the effectiveness of the proposed strategy on a simulation example, where the proposed fixed-time stabilizing low-level controller shows successful satisfaction of control objectives, whereas an exponentially stabilizing low-level controller fails.

Bib

@article{DBLP:journals/csysl/GargCRAP22,
  author       = {Kunal Garg and
                  Ryan K. Cosner and
                  Ugo Rosolia and
                  Aaron D. Ames and
                  Dimitra Panagou},
  title        = {Multi-Rate Control Design Under Input Constraints via Fixed-Time Barrier
                  Functions},
  journal      = {{IEEE} Control. Syst. Lett.},
  volume       = {6},
  pages        = {608--613},
  year         = {2022},
  url          = {https://doi.org/10.1109/LCSYS.2021.3084322},
  doi          = {10.1109/LCSYS.2021.3084322},
  timestamp    = {Thu, 16 Sep 2021 18:02:01 +0200},
  biburl       = {https://dblp.org/rec/journals/csysl/GargCRAP22.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}