Minimum-Time/Energy, Output Transitions for Dual-Stage Systems

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.