Adaptive sliding mode control of uncertain noholonomic systems with unknown control direction

In this paper, an adaptive sliding mode control scheme capable of solving the problem of stabilizing a class of nonholonomic systems in chained form with unknown control direction affected by uncertain nonlinear drift term and parametric uncertainties is proposed. The crucial point is the necessity of reformulating the system model so as to make the uncertain terms appear in matched form. The system model transformation proposed in this paper is based on a discontinuous state scaling and a backstepping based transformation. Then, relying on the new system states, it is possible to design an appropriate parameter adaptation mechanism and a particular sliding manifold. The control scheme proposed in this paper is capable of enforcing a sliding mode on the selected manifold without the knowledge of the sign of the control gain. The advantage of this proposal relies on its applicability to nonholonomic systems with unknown control direction also in presence of a significant class of uncertainties.