Adaptive Nonlinear W∞ Control for Fully Actuated Mechanical Systems

Abstract

This work proposes an adaptive nonlinear W∞ controller for fully actuated mechanical systems operating under the influence of parametric uncertainties and external disturbances. The controller is designed through the novel W∞ control approach, which extends the formulation of the H∞ control theory to the weighted Sobolev spaces, providing faster disturbance attenuation with improved transient performance to the closed-loop system. Additionally, update laws are proposed to estimate uncertain parameters and external disturbances, improving the performance with ensured stability. Comparative analysis between the proposed adaptive nonlinear W∞ controller, an adaptive H∞ one, and the classic nonlinear W∞ controller is performed to highlight the advantages of the proposed approach.