Stabilization of Nonlinear Systems through Control Barrier Functions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917750992011264 |
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| author | Mestres, Pol Long, Kehan Leok, Melvin Atanasov, Nikolay Cortes, Jorge |
| author_facet | Mestres, Pol Long, Kehan Leok, Melvin Atanasov, Nikolay Cortes, Jorge |
| contents | This paper proposes a control design approach for stabilizing nonlinear control systems. Our key observation is that the set of points where the decrease condition of a control Lyapunov function (CLF) is feasible can be regarded as a safe set. By leveraging a nonsmooth version of control barrier functions (CBFs) and a weaker notion of CLF, we develop a control design that forces the system to converge to and remain in the region where the CLF decrease condition is feasible. We characterize the conditions under which our controller asymptotically stabilizes the origin or a small neighborhood around it, even in the cases where it is discontinuous. We illustrate our design in various examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08398 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabilization of Nonlinear Systems through Control Barrier Functions Mestres, Pol Long, Kehan Leok, Melvin Atanasov, Nikolay Cortes, Jorge Optimization and Control Systems and Control This paper proposes a control design approach for stabilizing nonlinear control systems. Our key observation is that the set of points where the decrease condition of a control Lyapunov function (CLF) is feasible can be regarded as a safe set. By leveraging a nonsmooth version of control barrier functions (CBFs) and a weaker notion of CLF, we develop a control design that forces the system to converge to and remain in the region where the CLF decrease condition is feasible. We characterize the conditions under which our controller asymptotically stabilizes the origin or a small neighborhood around it, even in the cases where it is discontinuous. We illustrate our design in various examples. |
| title | Stabilization of Nonlinear Systems through Control Barrier Functions |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2408.08398 |