Adaptive Control Barrier Functions with Vanishing Conservativeness Under Persistency of Excitation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913581465862144 |
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| author | Gutierrez, Ricardo Hoagg, Jesse B. |
| author_facet | Gutierrez, Ricardo Hoagg, Jesse B. |
| contents | This article presents a closed-form adaptive controlbarrier-function (CBF) approach for satisfying state constraints in systems with parametric uncertainty. This approach uses a sampled-data recursive-least-squares algorithm to estimate the unknown model parameters and construct a nonincreasing upper bound on the norm of the estimation error. Together, this estimate and upper bound are used to construct a CBF-based constraint that has nonincreasing conservativeness. Furthermore, if a persistency of excitation condition is satisfied, then the CBFbased constraint has vanishing conservativeness in the sense that the CBF-based constraint converges to the ideal constraint corresponding to the case where the uncertainty is known. In addition, the approach incorporates a monotonically improving estimate of the unknown model parameters thus, this estimate can be effectively incorporated into a desired control law. We demonstrate constraint satisfaction and performance using 2 two numerical examples, namely, a nonlinear pendulum and a nonholonomic robot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12899 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive Control Barrier Functions with Vanishing Conservativeness Under Persistency of Excitation Gutierrez, Ricardo Hoagg, Jesse B. Systems and Control This article presents a closed-form adaptive controlbarrier-function (CBF) approach for satisfying state constraints in systems with parametric uncertainty. This approach uses a sampled-data recursive-least-squares algorithm to estimate the unknown model parameters and construct a nonincreasing upper bound on the norm of the estimation error. Together, this estimate and upper bound are used to construct a CBF-based constraint that has nonincreasing conservativeness. Furthermore, if a persistency of excitation condition is satisfied, then the CBFbased constraint has vanishing conservativeness in the sense that the CBF-based constraint converges to the ideal constraint corresponding to the case where the uncertainty is known. In addition, the approach incorporates a monotonically improving estimate of the unknown model parameters thus, this estimate can be effectively incorporated into a desired control law. We demonstrate constraint satisfaction and performance using 2 two numerical examples, namely, a nonlinear pendulum and a nonholonomic robot. |
| title | Adaptive Control Barrier Functions with Vanishing Conservativeness Under Persistency of Excitation |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2411.12899 |