This article addresses the optimal (minimum-time/energy) trajectory design for changing the output from one value y̱ to another y¯ within a finite time interval [0,tf] called the output-transition time interval. The output should be maintained constant (at the desired value) outside the output-transition time interval. The main contribution of this article is to establish the existence of a solution to the problem when preactuation (input applied during time t<0) and postactuation (input applied during time t>tf) are allowed. The advantage of using pre- and postactuation inputs is illustrated with an experimental dual-stage actuator system.

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