Flop: feedback local optimality control of the inverse pendulum oscillations

Feedback control techniques for vibrations suppression are widely investigated in the technical literature. However, the most powerful method in this context, the optimal control theory, despites its generality and flexibility related to the user defined cost function, meets serious engineering limitations. This is due to the lack of a feedback law, because of the intrinsic formulation of the Pontryagin optimality criterion. This paper proposes a novel method of control that, still maintaining the structure of the optimal control technique, provides a feedback control. The method is applied to one of the most challenging nonlinear oscillation control, the inverse pendulum, that is a benchmark in the field. The FLOP- Feedback Local OPtimality control, provides excellent results obtaining with a unique control law a very rapid swing-up of the pendulum and its inverse position characterized by instable vibrations is maintained by the FLOP control in a more efficient way with respect to competitor recent methods.