Discrete time immersion and invariance adaptive control via partial state feedback for systems in block strict feedback form

This paper presents a new method for the adaptive (tracking) regulation via partial state feedback for a class of discrete-time nonlinear systems in parametric strict-feedback form. A procedure is proposed based on immersion and invariance control approach where the parameter estimator and state observer designs are accomplished simultaneously. The algorithm utilizes discrete-time adaptive backstepping in the controller construction while providing a design without over parametrization. The proposed controller construction guarantees boundedness of the closed-loop trajectories and global (tracking) convergence to the origin of the state of the closed-loop system. The performance of the proposed method is illustrated by simulations.