Control of pendulum oscillations with variable parameters

Two pendulum control problems are considered, in which oscillations are excited by changing the length (or the position of the center of mass) of the pendulum or by displacing the suspension point. The control objective is approaching a certain invariant set in the state space of the system. The solution approach is based on the speed gradient method. The obtained results make it possible to determine the domain of initial data and parameters on which the system possesses the desired properties.