Perturbed Integrators Chain Control via Barrier Function Adaptation and Lyapunov Redesign
<|reference_start|>Perturbed Integrators Chain Control via Barrier Function Adaptation and Lyapunov Redesign: 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.<|reference_end|>
@article{estrada2024perturbed,
    title={Perturbed Integrators Chain Control via Barrier Function Adaptation and
  Lyapunov Redesign},
    author={Manuel A. Estrada, Claudia A. P'erez-Pinacho, Christopher D.
  Cruz-Ancona, Leonid Fridman},
    journal={arXiv preprint arXiv:2405.09438},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.09438},
    primaryClass={eess.SY cs.SY}
}