  In this paper we discuss the controllability of two-point boundary value
problem (TBVP) for one-dimensional wave equation. Some new concepts are
introduced: TBVP input control problem, minimum-input solution (MS) and
pre-minimum-input solution (PMS). We set the metric in $L^1$ and $L^2$ spaces
on a closed set, and control the input to reach its minimum. And we mainly
discuss the property of input, the existence and uniqueness of MS and PMS for
$L^1$ and $L^2$ metric respectively. The minimum inputs lie on a strip in $L^1$
and PMS for $L^1$ and $L^2$ always exists. Furthermore, to construct PMS, we
also introduce an approximation method which meets certain conditions.
