ИСТИНА

https://www.com.uni-rostock.de/workshops/swim-2018/ A generalized formulation of optimal control problems for longitudinal motions of an elastic rod is studied. The only control input is a force applied at one end of the rod. Based on the Ritz method, a finite element algorithm is developed with piecewise polynomial approximations in the space-time domain for unknown displacement, momentum, and force fields. The control strategy aims to depress elastic vibrations in the rod. This is attained by minimizing both mean and terminal energies of the structure over a fixed time horizon. The results of numerical simulations for the case of nonuniform distribution of mechanical parameters are presented. The verification of optimal control laws has been performed taking into account the explicit local and integral error estimates obtained in accordance with the MIDR.