Many flexible structures consist of a large number of components coupled en
d to end in the form of a chain. In this study, the authors consider a type
of such structures formed by N one-dimensional coupled structures, with (N
- 1) controllers at the coupled points. A method of solution for such a sp
ecial class of optimal control problems is suggested by using an eigenfunct
ion expansion and the:maximum principle. This solution involves reducing th
e original problem to a system of ordinary differential equations. For comp
arative studies, the special problem is also solved by the variational appr
oach, which leads to a system of integral equations as a necessary and suff
icient condition of optimality. The effectiveness of these approaches is de
monstrated by means of a numerical solution for controlling the vibrations
of two strings that are coupled at the connecting point.