Abstract The paper deals with the optimal control of a distributed host structure consisting of two elastically connected complex continuous double-string system and subjected to certain excitation load. Investigation of the behavior of such system is of great theoretical and practical importance. A technique is proposed to actively damp out the undesired vibrations in the structures by a combination of applied actuators and displacement feedback gains. Two performance measures, involving energies at the terminal time as well as applied and feedback control efforts, are introduced. The optimality conditions of the applied actuators are derived by using the method of eigenfunction expansion and calculus of variations. The feedback parameters are numerically determined from the solution of a minimization problem. The proposed approach is illustrated by a numerical example involving a system which consists of two strings subjected to a continuous load.