@article{Park2023, 
author = {Hae Yeon Park and Jung Hoon Kim},
title = {Model-free control approach to uncertain Euler-Lagrange equations with a Lyapunov-based        L    ∞  -gain analysis},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {17666-17686},
keywords = {Lyapunov function, model-free control, L∞-gain, optimal tracking control, Euler-Lagrange equations, input-to-state stability (ISS)},
url = {https://www.sciopen.com/article/10.3934/math.2023902},
doi = {10.3934/math.2023902},
abstract = {This paper considers a model-free control approach to Euler-Lagrange equations and proposes a new quantitative performance measure with its Lyapunov-based computation method. More precisely, this paper aims to solve a trajectory tracking problem for uncertain Euler-Lagrange equations by using a model-free controller with a proportional-integral-derivative (PID) control form. The        L    ∞  -gain is evaluated for the closed-loop systems obtained through the feedback connection between the Euler-Lagrange equation and the model-free controller. To this end, the input-to-state stability (ISS) for the closed-loop systems is first established by deriving an appropriate Lyapunov function. The study further extends these arguments to develop a computational approach to determine the        L    ∞  -gain. Finally, the theoretical validity and effectiveness of the proposed quantitative performance measure are demonstrated through a simulation of a    2-degree-of-freedom (   2-DOF) robot manipulator, which is one of the most representative examples of Euler-Lagrange equations.}
}