An Adaptive Nonlinear $\mathcal{H}_{\infty}$ Control with Exact Parameter Estimation for Mechanical Systems

While exact parameter estimation is desired in numerous applications, many adaptive controllers require the fulfillment of the persistency of excitation (PE) condition to achieve that objective. Relaxing the PE condition poses a challenging theoretical problem and many research works have been devoted to addressing this issue. In this paper, we propose a novel adaptive robust nonlinear
$\mathcal{H}_{\infty}$
optimal controller for trajectory tracking of mechanical systems subjected to unknown parameters. The proposed method includes an extra term, based on the dynamic regressor extension and mixing (DREM) approach, into the adaptive law which enables exact parameter estimation even without fulfilling the PE condition. The effectiveness of the proposed adaptive controller is corroborated with numerical experiments involving a CRS-A465 robot manipulator and comparison analyses with a classic adaptive nonlinear
$\mathcal{H}_{\infty}$
controller.