Higher order supertwisting algorithm for perturbed chains of integrators of arbitrary order

In this paper, we present a generalization for the supertwisting algorithm for perturbed chains of integrators of arbitrary order. This Higher Order Supertwisting (HOST) controller, which extends the approach of [1], is either continuous or quasi-continuous and its design is derived from a first result obtained for pure chains of integrators, the latter relying on a geometric condition introduced in [2], [3]. The complete result is established using a weak Lyapunov function and homogeneity arguments. The effectiveness of the controller is finally illustrated with simulations for a chain of integrator of order four where we compare the performances of a continuous HOST with those of a quasi-continous one.