Probabilistic Safety under Arbitrary Disturbance Distributions

@article{Teuwen2025-pz,
  title         = "Probabilistic safety under arbitrary disturbance
                  distributions using piecewise-affine control barrier
                  functions",
  author        = "Teuwen, Matisse and Schuurmans, Mathijs and Patrinos,
                  Panagiotis",
  abstract      = "We propose a simple safety filter design for stochastic
                  discrete-time systems based on piecewise affine
                  probabilistic control barrier functions, providing an
                  appealing balance between modeling flexibility and
                  computational complexity. Exact evaluation of the safety
                  filter consists of solving a mixed-integer quadratic program
                  (MIQP) if the dynamics are control-affine (or a
                  mixed-integer nonlinear program in general). We propose a
                  heuristic search method that replaces this by a small number
                  of small-scale quadratic programs (QPs), or nonlinear
                  programs (NLPs) respectively. The proposed approach provides
                  a flexible framework in which arbitrary (data-driven)
                  quantile estimators can be used to bound the probability of
                  safety violations. Through extensive numerical experiments,
                  we demonstrate improvements in conservatism and computation
                  time with respect to existing methods, and we illustrate the
                  flexibility of the method for modeling complex safety sets.
                  Supplementary material can be found at
                  https://mathijssch.github.io/ecc26-supplementary/.",
  month         =  dec,
  year          =  2025,
  archivePrefix = "arXiv",
  primaryClass  = "math.OC",
  eprint        = "2512.04194"
}