On Stabilization of Energy of a Conservative System Perturbed by a Random Process of “White-Noise” Type in the Itô Form

Abstract

We investigate the problem of deterministic control over the behavior of the total energy of the simplest conservative nonlinear system with one degree of freedom without friction in the case of random perturbations by a process of the “white-noise” type in the Itô form. These perturbations act under a fixed angle to the vector of phase velocity of the conservative system.