PV (Photovoltaic) cells have nonlinear current-voltage (I - V) and power-voltage (P - V) characteristics with a distinct maximum power point (MPP) that entirely depends on the ambient meteorological conditions (i.e. solar irradiance and temperature). Hence, to continuously extract and deliver the maximum possible power from the PV system, under given meteorological conditions, the maximum power point tracking (MPPT) control strategy needs to be formulated that continuously operates the PV system at its MPP. To achieve this goal, a hybrid nonlinear, very fast and efficient MPPT control strategy, based on the robust integral backstepping (RIB) control, is formulated in this research article. The simulation testbed comprises a standalone PV array, a non-inverting buck-boost (NIBB) DC-DC power converter, a purely resistive and a dynamic load (sound system). The proposed MPPT control scheme consists of two loops, where the first loop generates the real-time offline reference peak power voltage through an adaptive neuro-fuzzy inference system (ANFIS) network, which is then utilized in the second loop as a set-point value for generating a control signal and then forcing the PV system to be operated at this set-point by continuously adjusting the duty ratio of the power converter. This control strategy exhibits no overshoot, fast convergence, good transient response, fast rising and settling times and minimum output tracking error. The MATLAB/Simulink platform is used to test the performance of the proposed MPPT strategy against varying meteorological conditions, plant current and voltage faults and plant parametric uncertainties. To validate the superiority of the proposed control strategy, a comparative analysis of the proposed control strategy is presented with the nonlinear backstepping (B), integral backstepping controller (IB) and conventional PID and P&O based MPPT controllers.