Relaxing the high-frequency gain sign assumption in direct model reference adaptive control

A new, high performance, solution to the classical problem of direct model reference adaptive control for linear time-invariant systems with unknown sign of the high frequency gain is reported in the paper. The proposed algorithm directly estimates this parameter with the only required prior knowledge of a lower bound on its absolute value. To avoid the possible appearance of singularities in the controller calculation a switched projection mechanism is introduced to change, if needed, the sign of the estimate. The recently introduced dynamic regressor extension and mixing estimator is used to ensure monotonicity of the estimation error of the high frequency gain, guaranteeing that the switching appears (at most) once and avoiding the possible appearance of chattering-that may happen in classical gradient-based algorithms. Comparative simulations with the Nussbaum gain-based and gradient estimators illustrate the dramatic performance improvement of the proposed controller.