Barrier function-based adaptive higher order sliding mode controllers

Salah Laghrouche (1) , Mohamed Harmouche (2) , Yacine Chitour (3) , Hussein Obeid (4) , Leonid M Fridman (5)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 Actility - Actility
3 L2S - Laboratoire des signaux et systèmes
4 LUSAC - Laboratoire Universitaire des Sciences Appliquées de Cherbourg
5 UNAM - Universidad Nacional Autónoma de México = National Autonomous University of Mexico

In this paper, we present barrier function-based adaptive controllers for fast stabilization of a perturbed chain of integrators with bounded uncertainties. We refer to such controllers as adaptive higher order sliding mode controllers since they are designed for a perturbed chain of integrators of length r with bounded uncertainties such that the uncertainty bounds are unknown. We propose an adaptive control feedback law insuring the following: We provide a barrier function based adaptive controller ensuring the finite-time convergence of solutions to a desired vicinity of origin. Moreover, the homogeneity norm of solutions asymptotically tends to zero. The effectiveness of these controllers is illustrated through simulations

Domaines: Energie électrique; Thermique [physics.class-ph]; Automatique / Robotique; Mécanique des fluides [physics.class-ph]

Salah Laghrouche, Mohamed Harmouche, Yacine Chitour, Hussein Obeid, Leonid M Fridman. Barrier function-based adaptive higher order sliding mode controllers. Automatica, 2021, 123, pp.109355. ⟨10.1016/j.automatica.2020.109355⟩. ⟨hal-03456381⟩