Adaptive control of a class of nonlinear discrete-time systems

We consider adaptive control via state feedback for a class of feedback linearizable discrete-time systems. To parallel the development in adaptive nonlinear continuous-time control, we employ a systematic procedure to design the controllers and the update laws for the so-called parametric-strict-feedback form and the parametric-pure-feedback form. The geometric conditions that characterize this class of systems are given. Depending on the growth conditions of the nonlinearities, global boundedness and convergence are achieved with various update laws. We also develop adaptive indirect schemes with an observer-based identifier for the parametric-strict-feedback form. As a result, the drawback of overparametrization in direct schemes can be removed.