Practical stabilization of perturbed integrator chains with unknown bounds

2016/07/10 by Yacine Chitour, Chitour, Yacine, Mohamed Harmouche +3
Engineering · #Adaptive Control of Nonlinear Systems #Advanced Control Systems Optimization #Control and Stability of Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1607.02767

openalex publication_date 2016/07/10 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

In this paper, we present Lyapunov-based adaptive controllers for the practical (or real) stabilization of a perturbed chain of integrators with bounded uncertainties. We refer to such controllers as Adaptive Higher Order Sliding Mode (AHOSM) controllers since they are designed for nonlinear SISO systems with bounded uncertainties such that the uncertainty bounds are unknown. Our main result states that, given any neighborhood N of the origin, we determine a controller insuring, for every uncertainty bounds, that every trajectory of the corresponding closed loop system enters N and eventually remains there. The effectiveness of these controllers is illustrated through simulations.

Citations

• Sliding order and sliding accuracy in sliding mode control
• New methodologies for adaptive sliding mode control
• Adaptive continuous higher order sliding mode control

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