ИСТИНА

The paper is devoted to modeling and optimal control of longitudinal motions for a rectilinear elastic rod with distributed applied on its sides. The control inputs are the normal force, which is piecewise constant along the rod, as well as the external loads at its ends. It is assumed that the intervals of constancy in the normal force have equal length. Given initial and terminal states with a fixed time horizon, the optimal control problem is to minimize the mean mechanical energy stored in the rod. For the uniform rod, the minimal controllability time is found, and the exact optimal control law is designed in a recurrent way. The resulting control strategy is discussed, and the energy properties of the optimal solution are analyzed.