Tracking and parameter identification for model reference adaptive control

We provide barrier Lyapunov functions for model reference adaptive control algorithms, allowing us to prove robustness in the input-to-state stability framework and to compute rates of exponential convergence of the tracking and parameter identification errors to zero. Our results ensure identification of all entries of the unknown weight and control effectiveness matrices. We provide easily checked sufficient conditions for our relaxed persistency of excitation conditions to hold. Our illustrative numerical example demonstrates the performance of the control methods.