Universal Barrier Functions for Safety and Stability of Constrained Nonlinear Systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866908624760078336 |
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| author | Zinage, Vrushabh Bakolas, Efstathios |
| author_facet | Zinage, Vrushabh Bakolas, Efstathios |
| contents | In this paper, we address the problem of synthesizing safe and stabilizing controllers for nonlinear systems subject to complex safety specifications and input constraints. We introduce the Universal Barrier Function (UBF), a single continuously differentiable scalar-valued function that encodes both stability and safety criteria while accounting for input constraints. Using the UBF, we formulate a Quadratic Program (UBF-QP) to generate control inputs that are both safe and stabilizing under input constraints. We demonstrate that the UBF-QP is feasible if a UBF exists. Furthermore, under mild conditions, we prove that a UBF always exists. The proposed framework is then extended to systems with higher relative degrees. Finally, numerical simulations illustrate the effectiveness of our proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Barrier Functions for Safety and Stability of Constrained Nonlinear Systems Zinage, Vrushabh Bakolas, Efstathios Systems and Control In this paper, we address the problem of synthesizing safe and stabilizing controllers for nonlinear systems subject to complex safety specifications and input constraints. We introduce the Universal Barrier Function (UBF), a single continuously differentiable scalar-valued function that encodes both stability and safety criteria while accounting for input constraints. Using the UBF, we formulate a Quadratic Program (UBF-QP) to generate control inputs that are both safe and stabilizing under input constraints. We demonstrate that the UBF-QP is feasible if a UBF exists. Furthermore, under mild conditions, we prove that a UBF always exists. The proposed framework is then extended to systems with higher relative degrees. Finally, numerical simulations illustrate the effectiveness of our proposed approach. |
| title | Universal Barrier Functions for Safety and Stability of Constrained Nonlinear Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2511.01067 |