Direct discrete-time adaptive control with guaranteed parameter error convergence

A direct adaptive nonlinear tracking control framework for discrete-time multivariable nonlinear uncertain systems is developed. The proposed adaptive controller guarantees attraction of the closed-loop error dynamics in the face of parametric system uncertainty. In addition, parameter error convergence is also guaranteed when a generic geometric constraint holds on the update error gain matrix function. This condition is shown to be consistent with the notion of persistent excitation in the adaptive control and system identification literature required for parameter error convergence. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.