A backstepping-like approach to adaptive control in discrete time

Nonlinear adaptive control in discrete time is still largely open. The existing results deal with particular cases and are mainly based upon traditional estimation techniques issued from the linear literature. In this paper, combining a backstepping strategy and "a posteriori" estimation concepts, a novel approach for achieving adaptive stabilization is proposed. It can directly be applied to a class of nonlinear discrete-time systems that, analogous to the continuous-time context, are said to be in a parametric strict-feedback form. Necessary, and sufficient geometric-conditions guaranteeing the equivalence of a general discrete-time dynamics to the parametric strict-feedback form or to some related classes of dynamics are also proposed.