Immersion and invariance adaptive control for discrete time systems in strict feedback form

This paper presents a new design procedure for the adaptive regulation (tracking) via state feedback for discrete-time nonlinear systems in a parametric strict-feedback form. The algorithm utilizes discrete-time adaptive backstepping together with a new parameter estimator design. This approach provides an adaptive control law which guarantees boundedness of the closed-loop trajectories, global convergence to the origin (tracking) of the state of the closed-loop system, and local stability. The performance of the proposed method is illustrated by simulations.