Generation of virtual reference for discrete system by learning

Virtual reference is defined as the setpoint for a closed loop system so that the response tracks the desired path perfectly. It is proposed to obtain a virtual reference for a discrete system by repetitively modifying setpoint over the timed interval in which the desired path is specified. A necessary and sufficient condition that the response tracks perfectly is given firstly. In this learning method, a virtual response should be determined by learning when a new desired response should be considered. Secondly to improve this shortcoming is studied.