Safe Control of Semi-Explicit Differential-Algebraic Systems: Control Barrier Functions with SOS Verification
Abstract
Differential-algebraic equation (DAE) systems arise in power networks, multibody mechanics, and chemical processes, where algebraic constraints couple dynamic and algebraic states. Standard control barrier function (CBF) methods, designed for ordinary differential equations, fail for DAE systems because the algebraic constraints impose compatibility requirements that may render safety filters infeasible. This paper develops a safety-critical control framework for semi-explicit DAE systems using CBFs that consider compatibility with the algebraic constraints, termed DAE-aware CBFs. We construct projected vector fields on the constraint manifold to account for the hidden dynamics, while ensuring compatibility conditions that keep the algebraic constraints satisfied. We then present sum of squares (SOS) verification conditions that certify both correctness and feasibility of the resulting DAE-aware CBF. The framework is validated on power system case studies.
Related
- Differential Recursions, Projective Discriminants, and Algebraic Generating Functions
- Deterministic Non-Smooth Safety via Dual-Algebraic Control Barrier Functions
- Explicit and asymptotically good constructions of Algebraic Geometry codes in the sum-rank metric
- Computational verification of the Riemann hypothesis via differential equations
- Explicit matrix hitting points for noncommutative algebraic branching programs
BibTeX
@misc{kazma2026safe,
title = {{Safe Control of Semi-Explicit Differential-Algebraic Systems: Control Barrier Functions with SOS Verification}},
author = {Mohamad H. Kazma and Hongchao Zhang and Abdallah A. Albustami and Ben Wooding and Meiyi Ma and Taylor T. Johnson and Ahmad F. Taha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09634},
eprint = {2610.09634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09634},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Safe Control of Semi-Explicit Differential-Algebraic Systems: Control Barrier Functions with SOS Verification
AU - Mohamad H. Kazma
AU - Hongchao Zhang
AU - Abdallah A. Albustami
AU - Ben Wooding
AU - Meiyi Ma
AU - Taylor T. Johnson
AU - Ahmad F. Taha
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09634
UR - https://arxiv.org/abs/2610.09634
AB - Differential-algebraic equation (DAE) systems arise in power networks, multibody mechanics, and chemical processes, where algebraic constraints couple dynamic and algebraic states. Standard control barrier function (CBF) methods, designed for ordinary differential equations, fail for DAE systems because the algebraic constraints impose compatibility requirements that may render safety filters infeasible. This paper develops a safety-critical control framework for semi-explicit DAE systems using CBFs that consider compatibility with the algebraic constraints, termed DAE-aware CBFs. We construct projected vector fields on the constraint manifold to account for the hidden dynamics, while ensuring compatibility conditions that keep the algebraic constraints satisfied. We then present sum of squares (SOS) verification conditions that certify both correctness and feasibility of the resulting DAE-aware CBF. The framework is validated on power system case studies.
ER -