Exact tracking using backstepping control design and high-order sliding modes

In this technical note, a controller ensuring exponential exact tracking in the presence of matched and unmatched disturbances for the nonlinear systems in the block controllable form is proposed. The controller is designed using the backstepping procedure and combines the feedback linearization technique with the high-order sliding-modes. The matched and unmatched disturbances are compensated by the injection of a continuous term generated by the robust exact high-order sliding-modes differentiator. The obtained control law is differentiable and can be applied directly to the system. Simulations verify the performance of the proposed controller.