Model reference adaptive control: A finite-time approach

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.