Control of a class of mechanical systems with uncertainties via a constructive adaptive/second order VSC approach

A wide class of mechanical systems with uncertainties can be modeled through a state equation in parametric-pure-feedback form. Thus, in principle, the well-known backstepping design procedure can be applied to solve a regulation or a tracking problem. Yet, this is no more possible if a clear parametric dependence on the control signal (torque or force) cannot be established. Systems to which this happens can be efficaciously controlled via the proposed approach which inherits n-1 steps of the classical backstepping procedure. This latter procedure is used to attain a partial system state transformation, completed with the construction of a suitable sliding manifold upon which a second order sliding mode is enforced.