High-gain differentiators-based backstepping control of uncertain nonlinear systems using adaptive derivative-free control

This paper proposes an adaptive backstepping control design that incorporates high-gain differentiators (HGD) and a derivative-free (DF) adaptive control approach. First, the HGD addresses the ‘explosion of terms’ problem inherent in traditional backstepping by directly providing the required derivatives of virtual control inputs, thereby eliminating the need for analytical differentiation and reducing controller complexity. Next, a novel approximation technique based on a derivative-free adaptive learning structure is introduced to effectively handle both matched and mismatched uncertainties. Lyapunov-Krasovskii stability analysis is employed to ensure the boundedness of all closed-loop error signals. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.