Patent ID: 7035042

Claim:
A method for controlling an element that is part of a system so that for an instance in which it is necessary to reposition the element, the element is moved between a first position and a second position during a transition-time interval, and so that the element only moves during the transition-time interval and is precisely positioned both immediately before and after the transition-time interval, comprising the steps of: (a) providing a model of the system; (b) using the model for characterizing internal dynamics of the system in which energy applied to the system outside the transition-time interval is hidden so that the element does not move, other than during the transition-time interval; (c) for a selected optimization criterion, determining optimal internal states at a beginning and an end of a movement of the element between the first position and the second position; and (d) based upon the optimal internal states, determining an optimal control input signal for a transition-interval input, and at least one of a pre-actuation input and a post-actuation input acting on the element to cause the element to move from the first position to the second position so as to achieve the selected optimization criterion, wherein the pre-actuation input applies energy to the system before the transition-time interval, the post-actuation input applies energy to the system after the transition-time interval, and the transition-interval input applies energy to the system during the transition-time interval.