Gradient-based adaptive twisting-like algorithm with asymptotic convergence

This paper addresses the stabilization problem for a perturbed double-integrator affected by a bounded perturbation featuring a constant upperbound which is a priori unknown. We propose an adaptive feedback law, composed by the interconnection between a linear state-feedback controller and the twisting controller with two automatically tuned non-decreasing time-varying gains adjusted by gradient-based laws. A Lyapunov analysis, complemented by a Barbalat-based argument, is developed to certify the asymptotical stability of the closed loop system. The analysis provides a closed-form bound for the adaptive gains and it constructively yields simple design conditions for the controller parameters. We prove boundedness of all closed-loop signals and establish asymptotic convergence of both state variables to the origin without requiring prior knowledge of the disturbance bound. Simulation results are presented to corroborate the theoretical findings.