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arXiv · 2405.09438

Perturbed Integrators Chain Control via Barrier Function Adaptation and Lyapunov Redesign

Manuel A. Estrada·Claudia A. Pérez-Pinacho·Christopher D. Cruz-Ancona·Leonid Fridman
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Abstract

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.

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Manuel A. Estrada, Claudia A. Pérez-Pinacho, Christopher D. Cruz-Ancona, Leonid Fridman. 2024-05-15. Perturbed Integrators Chain Control via Barrier Function Adaptation and Lyapunov Redesign. https://arxiv.org/abs/2405.09438

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