Application of a constructive adaptive/second order VSC approach to a class of mechanical systems with uncertainties

A wide class of mechanical systems with uncertainties can be modelled through a state equation in parametric-pure-feedback form. In such a case the well-known backstepping design procedure can be applied to solve a regulation or a tracking problem. However, this will be impossible if a clear parametric dependence on the control signal (torque or force) cannot be established. Systems in partial parametric-pure-feedback form can be efficaciously controlled via the proposed approach which inherits n-2 steps of the classical backstepping procedure, attains a partial system state transformation, and associates with them the construction of a suitable sliding manifold upon which a second order sliding mode is enforced