Adaptive stabilisation of second-order strict-feedback systems based on FAS with tuning functions

Abstract

This paper thoroughly investigates adaptive stabilisation for a specific class of second-order strict-feedback nonlinear systems. Drawing inspiration from the fully actuated system (FAS) approach, an adaptive control scheme incorporating FAS with tuning functions is proposed. Notably, this approach directly addresses second-order systems without the need for reducing them to first-order systems, streamlining the intricate procedures involved. To handle uncertain parameters within the system, a combined scheme of adaptive estimation and tuning functions is employed. Rigorous analysis using Lyapunov stability theory demonstrates that the designed controller ensures the system's asymptotic convergence to the equilibrium point, with all other signals in the closed-loop system bounded. Finally, two simulation experiments verify the effectiveness of the proposed strategy: numerical simulations compared with sliding mode control and backstepping control, and practical application on the single-link robotic arm with a comparative analysis against backstepping control.