Model reference adaptive control: A finite‐time approach

Summary This article contributes with a finite‐time model reference adaptive control approach to solve the robust tracking problem for a class of disturbed scalar linear systems. A nonlinear continuous control law, composed of nonlinear adaptive gains, provides a finite‐time rate of convergence. For the ideal case, that is, without external disturbances, the tracking and the parameter (ideal control gains) identification error converge to zero in a finite time. For the disturbed case, the tracking and the parameter identification error dynamics are finite‐time input‐to‐state stable with respect to the external disturbance. The corresponding convergence proofs and the robustness analysis are based on a Lyapunov function approach, input‐to‐state stability theory, and homogeneity theory. Finally, simulation and experimental results show the feasibility of the proposed scheme.