Adaptive control of discrete time systems with concave/convex parametrizations

This note considers the adaptive control of a class of nonlinear discrete time system with concave/convex parametrizations. The solutions involved two tuning functions which are determined by a minmax optimization approach much like the continuous time counterparts found in the literature. Direct extension from the continuous time case do not work very well due to the premature termination of the adaptive algorithm before zero tracking error can be achieved. In this note, this problem is solved. The proposed algorithm is shown to be stable and achieves zero tracking error in steady state.