A Quadratic Program based Control Synthesis under Spatiotemporal Constraints and Non-vanishing Disturbances.

Abstract

In this paper, we study the effect of non-vanishing disturbances on the stability of fixed-time stable (FxTS) systems. We present a new result on FxTS, which allows a positive term in the time derivative of the Lyapunov function with the aim to model bounded, non-vanishing disturbances in system dynamics. We characterize the neighborhood to which the system trajectories converge, as well as the convergence time. Then, we use the new FxTS result and formulate a quadratic program (QP) that yields control inputs which drive the trajectories of a class of nonlinear, control-affine systems to a goal set in the presence of control input constraints and nonvanishing, bounded disturbances in the system dynamics. We consider an overtaking problem on a highway as a case study, and discuss how to both set up the QP and decide when to start the overtake maneuver in the presence of sensing errors.

Bib

@inproceedings{DBLP:conf/cdc/BlackGP20,
  author       = {Mitchell Black and
                  Kunal Garg and
                  Dimitra Panagou},
  title        = {A Quadratic Program based Control Synthesis under Spatiotemporal Constraints
                  and Non-vanishing Disturbances},
  booktitle    = {59th {IEEE} Conference on Decision and Control, {CDC} 2020, Jeju Island,
                  South Korea, December 14-18, 2020},
  pages        = {2726--2731},
  publisher    = {{IEEE}},
  year         = {2020},
  url          = {https://doi.org/10.1109/CDC42340.2020.9304071},
  doi          = {10.1109/CDC42340.2020.9304071},
  timestamp    = {Fri, 04 Mar 2022 13:31:02 +0100},
  biburl       = {https://dblp.org/rec/conf/cdc/BlackGP20.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}