Exact steering with arbitrarily bounded input for a class of driftless dynamics

Deals with the design of an arbitrarily bounded piecewise continuous control law for exact steering of systems which are feedback equivalent to nilpotent ones. On the basis of some results on exact and finite discretizability of dynamics, it is first shown that, for a nilpotent driftless dynamics the sampled equivalent one is a polynomial w.r.t. the products δu_i, where δ is the subinterval of the sampled time during which the control assumes a constant value, and u_i is the i-th input. This property brings us straightforwardly to the possibility of increasing δ in order to reduce u_i maintaining the product unchanged. The extension to driftless dynamics feedback equivalent to nilpotent ones passes through the exact computability of the state trajectory allowed by the finite discretizability property. An example is considered to show the effectiveness and the simplicity of the proposed technique