Barrier function-based stabilization of a perturbed chain of integrators with a predefined upperbound of the settling time

This paper proposes an adaptive time-varying approach for the stabilization of a class of perturbed chain of integrators with unknown control coefficient. To drive the trajectories initiating far from the origin, a time-varying feedback with adaptation is used, ensuring that the solutions of the closed loop system reach a prescribed vicinity of the origin within a finite-time, which is upper bounded by a prescribed time instant. Once the prescribed neighborhood is reached, a barrier function-based controller is used guaranteeing ultimate boundedness of the system’s solutions despite the presence of perturbations with unknown upper-bound. Numerical simulations on the stabilization problem of a third-order academic example show the effectiveness of the approach.