Paper
ReLU Barrier Functions for Nonlinear Systems with Constrained Control: A Union of Invariant Sets Approach
Authors
Pouya Samanipour, Hasan A. Poonawala
Abstract
Certifying safety for nonlinear systems with polytopic input constraints is challenging because CBF synthesis must ensure control admissibility under saturation. We propose an approximation--verification pipeline that performs convex barrier synthesis on piecewise-affine (PWA) surrogates and certifies safety for the original nonlinear system via facet-wise verification. To reduce conservatism while preserving tractability, we use a two-slope Leaky ReLU surrogate for the extended class-$\mathcal{K}$ function $α(\cdot)$ and combine multiple certificates using a Union of Invariant Sets (UIS). Counterexamples are handled through local uncertainty updates. Simulations on pendulum and cart-pole systems with input saturation show larger certified invariant sets than linear-$α$ designs with tractable computation time.
Metadata
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.15286v1</id>\n <title>ReLU Barrier Functions for Nonlinear Systems with Constrained Control: A Union of Invariant Sets Approach</title>\n <updated>2026-03-16T13:48:30Z</updated>\n <link href='https://arxiv.org/abs/2603.15286v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.15286v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Certifying safety for nonlinear systems with polytopic input constraints is challenging because CBF synthesis must ensure control admissibility under saturation. We propose an approximation--verification pipeline that performs convex barrier synthesis on piecewise-affine (PWA) surrogates and certifies safety for the original nonlinear system via facet-wise verification. To reduce conservatism while preserving tractability, we use a two-slope Leaky ReLU surrogate for the extended class-$\\mathcal{K}$ function $α(\\cdot)$ and combine multiple certificates using a Union of Invariant Sets (UIS). Counterexamples are handled through local uncertainty updates. Simulations on pendulum and cart-pole systems with input saturation show larger certified invariant sets than linear-$α$ designs with tractable computation time.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='eess.SY'/>\n <published>2026-03-16T13:48:30Z</published>\n <arxiv:comment>Accepted to ACC 2026</arxiv:comment>\n <arxiv:primary_category term='eess.SY'/>\n <author>\n <name>Pouya Samanipour</name>\n </author>\n <author>\n <name>Hasan A. Poonawala</name>\n </author>\n </entry>"
}