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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.15286 |
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| _version_ | 1866915867008172032 |
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| author | Samanipour, Pouya Poonawala, Hasan A. |
| author_facet | Samanipour, Pouya Poonawala, Hasan A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15286 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | ReLU Barrier Functions for Nonlinear Systems with Constrained Control: A Union of Invariant Sets Approach Samanipour, Pouya Poonawala, Hasan A. Systems and Control 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. |
| title | ReLU Barrier Functions for Nonlinear Systems with Constrained Control: A Union of Invariant Sets Approach |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2603.15286 |