Regimes Of More and More Frequent Switchings in the Optimal Control Problem of Oscillations of $n$ Oscillators

The paper considers the control system of $n$ oscillators executing forced oscillations under the action of a scalar-valued control force common for all oscillators whose module is bounded. The author proves the existence of an optimal singular regime and the assertion that the optimal control has at least countably many switchings that accumulate to a conjunction point of the singular and nonsingular parts of the trajectory.