Input shaping and time-optimal control of flexible structures. (Q1400327)

The authors observe the well-known fact that the optimal controls for linear time-invariant systems are bang-bang. For the systems considered by the authors the existence and uniqueness of the optimal solution has been proved. The Pontryagin version of Hamilton equations assures that a necessary condition for optimality is met. Convoluting the resulting control input with a sequence of discrete impulses is known as ``shaping the input''. If the result of such an action is a zero residual vibration, such a shaper is called a ZV (zero vibration) shaper. Conjectures were made, but a rigorous proof was absent, that in problems stated in the paper the time-optimal control and zero vibration input shaper are equivalent. The authors use the multiplier technique and some of their previously published results to prove this conjecture.