Safety of layered control systems via control barrier morphisms

@misc{ames2026safety,
  title = {{Safety of layered control systems via control barrier morphisms}},
  author = {Aaron D. Ames and Joe Moeller and Massimiliano de Sa and Paulo Tabuada},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38108},
  eprint = {2610.38108},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38108},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Safety of layered control systems via control barrier morphisms
AU  - Aaron D. Ames
AU  - Joe Moeller
AU  - Massimiliano de Sa
AU  - Paulo Tabuada
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38108
UR  - https://arxiv.org/abs/2610.38108
AB  - Layered control architectures provide a powerful paradigm for synthesizing controllers for complex systems. Yet, translating guarantees at each layer to system-level guarantees is challenging due to the interactions between layers. To address this problem, this paper presents a categorical perspective on layered control architectures. Individual systems are represented as control coalgebras, their interactions are specified as morphisms to mediators, and system-level behaviors are obtained via composition defined categorically as a pullback. To analyze the safety of these systems, we formulate control barrier morphisms (CBMs), the categorical generalization of control barrier functions. We prove that feedback controllers satisfying a CBM condition render the associated safe subobject forward invariant. It is through CBMs that we can establish the safety of layered systems: given a CBM at each layer subject to compatibility conditions, the universal property of the pullback implies the existence of a CBM for the composed system. Safety of a full-order model being safety filtered by a reduced-order model is recovered as a specialization of the categorical framework.
ER  -