Probabilistic stabilizability certificates for a class of black-box linear systems

Filippo Fabiani, Kostas Margellos and Paul J. Goulart

@article{FMG:2022b,
  author = {Filippo Fabiani and Kostas Margellos and Paul J. Goulart},
  title = {Probabilistic stabilizability certificates for a class of black-box linear systems},
  journal = {IEEE Control Systems Letters},
  year = {2022},
  volume = {6},
  pages = {584-589},
  url = {https://ieeexplore.ieee.org/document/9441020},
  doi = {10.1109/LCSYS.2021.3083962}
}

We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems generated by a possibly inexact quantification of some parameters in the state-space matrices. By exploiting a set of realizations of those undetermined parameters, verifying the controlled invariance property of the given set amounts to a linear program, whose feasibility allows us to establish an a-posteriori probabilistic certificate on the controlled invariance property of such a set with respect to the unknown linear time-invariant dynamics. We apply this framework to the control of a networked system with unknown weighted graph.