Perturbed Integrators Chain Control via Barrier Function Adaptation and Lyapunov Redesign
CoRR(2024)
摘要
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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