Robust Adaptive Nonlinear W_∞ Control for Mechanical Systems^*

This paper proposes a robust adaptive nonlinear optimal control strategy for mechanical systems that employs the weighted Sobolev space to achieve trajectory tracking with enhanced transient performance, even in the presence of parametric uncertainties and exogenous disturbances. The proposed adaptive ${{\mathcal{W}}_{\infty} }$ control law utilizes the Dynamic Regressor Extension and Mixing (DREM) estimator to estimate parameter values without relying on persistence of excitation (PE) conditions. Additionally, we use the concept of the Euler-Lagrange first integral to eliminate the need for acceleration measurements, which simplifies the application of DREM-based estimators. Numerical results involving a quadrotor unmanned aerial vehicle (UAV) are presented to corroborate the theoretical findings, demonstrating improved performance compared to a non-adaptive counterpart controller.