Direct adaptive control of discrete-time nonlinear systems using an input-output model

A direct adaptive tracking controller for a class of nonlinear discrete-time systems expressed in input-output form is developed. Using a state space representation, the linearizing input and the internal dynamics are obtained. By employing the projection algorithm the estimate of the unknown parameters are utilized in the linearization process. A Lyapunov analysis is used to show that under certain conditions (a priori lower and upper bound of the unknown parameters), the closed-loop adaptively controlled system is stable and moreover the tracking error converges to zero asymptotically. Finally, the simulation results are presented to illustrate the features of the proposed method.