Predefined-time adaptive backstepping control for a class of nonlinear dynamical systems with parametric uncertainties

In this article, we address the problem of achieving predefined-time control for a class of nonlinear dynamical systems with parameter uncertainties. We introduce an adaptive predefined-time control algorithm based on integrator backstepping for nth order nonlinear systems. Using Lyapunov's stability theory, we establish that the proposed predefined time control approach, combinedwith an adaptive law, ensures the boundedness of all signals within the closed-loop system. A notable advantage of our method is its potential to achieve convergence within a predetermined time frame. To validate our approach's efficacy, we present a practical example involving a 2 DOF helicopter, demonstrating the effectiveness of the proposed scheme.