Barriers and Potentially Safe Sets in Hybrid Systems: Pendulum with Non-Rigid Cable

Willem Esterhuizen (1) , Jean Lévine (1)

1 CAS - Centre Automatique et Systèmes

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.

Mots clés: Hybrid systems; Nonlinear systems; Safety sets; Control of constrained systems; State and input constraints; Mixed constraints; Admissible set; Barrier

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Willem Esterhuizen, Jean Lévine. Barriers and Potentially Safe Sets in Hybrid Systems: Pendulum with Non-Rigid Cable. Automatica, 2016, 73, pp.248-255. ⟨10.1016/j.automatica.2016.07.001⟩. ⟨hal-01549638⟩