Optimal Control for Nonlinear Oscillations of Natural Mechanical Systems

The problem of controlling oscillations in the vicinity of the equilibrium position of scleronomic mechanical systems with several degrees of freedom is solved. One degree of freedom is uncontrollable directly, and the rest are controlled by servos. Controllable coordinates can be both positional and cyclic. A method is proposed for finding the optimal control of the amplitude of oscillation in an uncontrollable degree of freedom. This method is based on an appropriate choice of a rule of change for the controllable degrees of freedom. The effectiveness of the proposed method is demonstrated by the example of a two-link pendulum.