This note studies a class of discrete-time nonlinear systems which depend on a small parameter. Using the singular perturbation theory in a systematic way, we give a trajectory approximation result based on the decomposition of the model into reduced and boundary layer models. This decomposition is used to analyze optimal control via maximum principle of such systems. As a result, significant order reduction of optimal control problems is achieved.
['Rachid Bouyekhf', 'A. El Hami', 'A. El Moudni']
Optimal control of a particular class of singularly perturbed nonlinear discrete-time systems