Perturbed Integrators Chain Control via Barrier Function Adaptation and Lyapunov Redesign
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911877347409920 |
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| author | Estrada, Manuel A. Pérez-Pinacho, Claudia A. Cruz-Ancona, Christopher D. Fridman, Leonid |
| author_facet | Estrada, Manuel A. Pérez-Pinacho, Claudia A. Cruz-Ancona, Christopher D. Fridman, Leonid |
| contents | Lyapunov redesign is a classical technique that uses a nominal control and its corresponding nominal Lyapunov function to design a discontinuous control, such that it compensates the uncertainties and disturbances. In this paper, the idea of Lyapunov redesign is used to propose an adaptive time-varying gain controller to stabilize a class of perturbed chain of integrators with an unknown control coefficient. It is assumed that the upper bound of the perturbation exists but is unknown. A proportional navigation feedback type gain is used to drive the system's trajectories into a prescribed vicinity of the origin in a predefined time, measured using a quadratic Lyapunov function. Once this neighborhood is reached, a barrier function-based gain is used, ensuring that the system's trajectories never leave this neighborhood despite uncertainties and perturbations. Experimental validation of the proposed controller in Furuta's pendulum is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09438 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perturbed Integrators Chain Control via Barrier Function Adaptation and Lyapunov Redesign Estrada, Manuel A. Pérez-Pinacho, Claudia A. Cruz-Ancona, Christopher D. Fridman, Leonid Systems and Control Lyapunov redesign is a classical technique that uses a nominal control and its corresponding nominal Lyapunov function to design a discontinuous control, such that it compensates the uncertainties and disturbances. In this paper, the idea of Lyapunov redesign is used to propose an adaptive time-varying gain controller to stabilize a class of perturbed chain of integrators with an unknown control coefficient. It is assumed that the upper bound of the perturbation exists but is unknown. A proportional navigation feedback type gain is used to drive the system's trajectories into a prescribed vicinity of the origin in a predefined time, measured using a quadratic Lyapunov function. Once this neighborhood is reached, a barrier function-based gain is used, ensuring that the system's trajectories never leave this neighborhood despite uncertainties and perturbations. Experimental validation of the proposed controller in Furuta's pendulum is presented. |
| title | Perturbed Integrators Chain Control via Barrier Function Adaptation and Lyapunov Redesign |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2405.09438 |