Tracking in nonholonomic dynamic systems via sliding modes

We use an approach based on sliding mode control to design a feedback which forces the state vector of a nonholonomic integrator to track the desired time function. A discontinuous feedback control is found which allows the ε-tracking in spite of the fact that the number of controls is less than the dimensionality of the tracking function. The developed approach is applied to a nonholonomic system which describes the motion of the rotating knife moving on the surface. A numerical example is considered