Fast adaptation for an uncertain nonlinear system using adaptive feedback linearization with optimal control modification

In this paper, we investigate an adaptive control for fast adaptation without high-frequency oscillation, using feedback linearization and optimal control modification. Generally, a large adaptive gain is used to achieve fast adaptation and this can cause high-frequency oscillations in standard model-reference adaptive control. The fast adaptation approach is based on an optimal control problem to minimize L₂ norm of the tracking error. Through the adaptive feedback linearization-based technique with first-order filters, optimal control modification can be applied to more general nonlinear systems having unmatched uncertainties. Uniformly ultimate boundedness of the overall closed-loop system is analyzed by the Lyapunov stability theory. Simulation results validate the performance of the proposed control approach.