A new finite-time convergent and robust direct model reference adaptive control for SISO linear time invariant systems

Abstract

The objective of this paper is to propose a new Direct MRAC (Model Reference Adaptive Control), having finite-time convergence of the tracking error and the parameter estimation algorithm under appropriate Persistence of Excitation Conditions. Moreover, enhanced robustness properties are also achieved. This is obtained by adding some strong, i.e. non locally Lipschitz or discontinuous, nonlinearities to the controller and parameter estimation algorithm of the classical MRAC. A Lyapunov-based approach is used to prove these properties. Some simulations illustrate how the proposed algorithm provides the MRAC with a much faster convergence of the tracking and parameter errors. Moreover, the improved convergence is obtained with less control action and with enhanced robustness properties of the control loop.