The present paper addresses the control and the power management of a hybrid system dedicated to an elevator application. In fact, the multi-source includes a photovoltaic generator as a main source supported by a battery-bank and a stack of super capacitors (SC). On the traction part, a permanent magnet synchronous motor (PMSM) is used to carry the elevator box. The power supervising mission is performed via a neural network (NN) routine trained with a frequency based strategy (FBS). The main objective of the applied control routines is to manage effectively the splits of the load demand. Therefore, they can provide the required power amounts in both steady-state and transient state, respecting the dynamic behavior of each source. Obviously, a fuzzy logic MPPT method has been applied to the PV side to permanently track the maximum power point through an adequate tuning of a boost converter regardless of the solar irradiance variations. Whereas, the controller of the DC-DC bidirectional converters of the battery and SC stack is based on the direct lyapunov theory. To test the effectiveness of the proposed techniques, intensive numerical tests are done using MATLAB/Simulink Package. The obtained results prove the feasibility of the proposed approach, where the system switches smoothly between the operating modes.