Skip to Main content Skip to Navigation

On Barriers in Constrained Nonlinear Systems with an Application to Hybrid Systems

Abstract : This thesis deals with the theory of barriers in input and state constrained nonlinear systems. Our main contribution is a generalisation to the case where the constraints are mixed, that is they depend on both the input and the state in a coupled way. Constraints of this type often appear in applications, as well as in constrained flat systems. We prove a minimum-like principle that allows the construction of the barrier and the associated admissible set. Moreover, in case of intersection of some of the trajectories involved in this principle, we prove that such transversal intersection points are stopping points of the barrier.We demonstrate the utility of all the theoretical contributions by finding the admissible set for the inverted pendulum on a cart with a non-rigid cable, the constraint being that the cable remains taut. Note that this problem corresponds to the determination of potentially safe sets in hybrid systems.
Document type :
Complete list of metadata

Cited literature [61 references]  Display  Hide  Download
Contributor : ABES STAR :  Contact
Submitted on : Tuesday, April 26, 2016 - 11:42:08 AM
Last modification on : Wednesday, November 17, 2021 - 12:31:03 PM
Long-term archiving on: : Wednesday, July 27, 2016 - 12:40:13 PM


Version validated by the jury (STAR)


  • HAL Id : tel-01307106, version 1


Willem Esterhuizen. On Barriers in Constrained Nonlinear Systems with an Application to Hybrid Systems. Automatic Control Engineering. Ecole Nationale Supérieure des Mines de Paris, 2015. English. ⟨NNT : 2015ENMP0061⟩. ⟨tel-01307106⟩



Record views


Files downloads