Analytic form of optimal boundary controls of transverse vibrations of a rod consisting of several parts with different densities and elasticities but with the same impedances

摘要

We consider the problem of optimal boundary displacement control (control minimizing the boundary energy functional) of an elastic rod consisting of several parts with different densities and elasticities but with the same impedances. We obtain a closed-form expression for the optimal control bringing the rod from an arbitrarily given initial state to an arbitrarily given terminal state in a given time T.