Barrier function-based adaptive higher order sliding mode controllers

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.