Adaptive multiple-surface sliding mode control of nonholonomic systems with matched and unmatched uncertainties

The problem of stabilizing a class of nonholonomic systems in chained form affected by both matched and unmatched uncertainties is addressed in this paper. The proposed design methodology is based on a discontinuous transformation of the perturbed nonholonomic system to which an adaptive multiple-surface sliding mode technique is applied. The generation of a sliding mode allows to eliminate the effect of matched uncertainties, while a suitable function approximation technique enables to deal with the residual uncertainties, which are unmatched. The control problem is solved by choosing a particular sliding manifold upon which a second order sliding mode is enforced via a continuous control with discontinuous derivative. A positive feature of the present proposal, apart from the fact of being capable of dealing with the presence of both matched and unmatched uncertainties, is that no knowledge of the bounds of the unmatched uncertainty terms is required. Moreover, the fact of producing a continuous control makes the proposed approach particularly appropriate in nonholonomic applications, such as those of mechanical nature.