Barriers and Potentially Safe Sets in Hybrid Systems: Pendulum with Non-Rigid Cable
arXiv:2109.10976 · doi:10.1016/j.automatica.2016.07.001
Abstract
This paper deals with an application of the notion of barrier in mixed constrained nonlinear systems to an example of a pendulum mounted on a cart with non-rigid cable, whose dynamics may switch to free-fall when the tension of the cable vanishes. We present a direct construction of the boundary of the potentially safe set in which there always exists a control such that the cable never goes slack. A discussion on the dependence of this set with respect to the pendulum and cart masses is then sketched.
10 pages, 5 figures, as published in Automatica