Formal Verification of Control Lyapunov-Barrier Functions for Safe Stabilization with Bounded Controls
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914156927516672 |
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| author | Liu, Jun |
| author_facet | Liu, Jun |
| contents | We present verifiable conditions for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety under bounded controls. These sufficient conditions ensure the strict compatibility of a control barrier function (CBF) and a control Lyapunov function (CLF) on the exact safe set certified by the barrier. An explicit smooth control Lyapunov-barrier function (CLBF) is then constructed via a patching formula that is provably correct by design. Two examples illustrate the computational procedure, showing that the proposed approach is less conservative than sum-of-squares (SOS)-based compatible CBF-CLF designs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_10510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formal Verification of Control Lyapunov-Barrier Functions for Safe Stabilization with Bounded Controls Liu, Jun Systems and Control Optimization and Control We present verifiable conditions for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety under bounded controls. These sufficient conditions ensure the strict compatibility of a control barrier function (CBF) and a control Lyapunov function (CLF) on the exact safe set certified by the barrier. An explicit smooth control Lyapunov-barrier function (CLBF) is then constructed via a patching formula that is provably correct by design. Two examples illustrate the computational procedure, showing that the proposed approach is less conservative than sum-of-squares (SOS)-based compatible CBF-CLF designs. |
| title | Formal Verification of Control Lyapunov-Barrier Functions for Safe Stabilization with Bounded Controls |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2511.10510 |