A $Q$-Modification Neuroadaptive Control Architecture for Discrete-Time Systems

This brief extends the new neuroadaptive control framework for continuous-time nonlinear uncertain dynamical systems based on a
Q
-modification architecture to discrete-time systems. As in the continuous-time case, the discrete-time update laws involve auxiliary terms, or
Q
-modification terms, predicated on an estimate of the unknown neural network weights which in turn involve a set of auxiliary equations characterizing a set of affine hyperplanes. In addition, we show that the
Q
-modification terms in the discrete-time update law are designed to minimize an error criterion involving a sum of squares of the distances between the update weights and the family of affine hyperplanes.