Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

In this study, a robust nonlinear L-infinity-gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L-infinity-gain optimal tracking control cannot be solved directly, the nonlinear L-infinity-gain optimal tracking problem is transformed into a nonlinear L-infinity-gain tracking problem by given a prescribed disturbance attenuation level for the L-infinity-gain tracking performance. To guarantee that the L-infinity-gain tracking performance can be achieved for the uncertain robotic systems, a sliding-mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew-symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L-infinity-gain tracking control problems in terms of all algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation call be solved analytically. Therefore, the proposed robust L-infinity-gain tracking control scheme is suitable for practical control design of uncertain robotic systems.