Nonsmooth feedback control for Lagrange systems with input saturation

For the motion control of a class of Lagrange systems, a new design method based on nonsmooth design technology is considered to overcome the input saturation of the system. The feedback gain of the controller is designed according to the different regions which the tracking errors belong to. Moreover, a sufficient condition is proposed to ensure that the output of the controller is within the constraint of the system. Then, the trade-off between the high gain feedback and the input constraint is realized. Shown by simulations, the new design is more effective than the usual designs.