Direct adaptive control for discrete-time nonlinear uncertain dynamical systems

A direct adaptive nonlinear control framework for discrete-time multivariable nonlinear uncertain systems with exogenous bounded disturbances is developed. The adaptive nonlinear controller addresses adaptive stabilization, disturbance rejection, and adaptive tracking. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the plant. Finally, two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.