Adaptive second order sliding mode control of uncertain nonholonomic systems

The problem of controlling a class of nonholonomic systems in chained form affected by uncertain nonlinear drift term and parametric uncertainties is addressed in this paper. The control of nonholonomic systems is a quite complex problem since this class of systems is not stabilizable with a stationary continuous state feedback. The idea investigated in this paper is to apply the so-called second order sliding mode control methodology to solve this problem. To this end, the system model needs to be reformulated so as to make the uncertain terms appear in matched form. A suitable transformation of the system model, based on a discontinuous state scaling and a backstepping based procedure, is proposed in the paper. On the basis of the transformed system state, it is possible to design an appropriate parameter adaptation mechanism and a particular sliding manifold upon which a second order sliding mode is enforced.