Output tracking for nonlinear systems is complicated by the existence of singular submanifolds." These are surfaces on which the decoupling matrix loses rank. To provide additional control action we identify a class of smooth vector fields whose integral curves can be incrementally tracked using rapidly switched piecewise constant controls. At discrete times the resulting piecewise smooth state trajectories approach the integral curve being tracked. These discontinuous controllers are applied to sliding mode control we use incremental tracking to move the state toward the sliding surface. The resulting controller achieves approximate output tracking in situations where the usual approach to sliding mode control fails due to the loss of control action on the singular submanifold.