In this work, a photovoltaic (PV) system integrated with a non-inverting DC-DC buck-boost converter to extract maximum power under varying environmental conditions such as irradiance and temperature is considered. In order to extract maximum power (via maximum power transfer theorem), a robust nonlinear arbitrary order sliding mode-based control is designed for tracking the desired reference, which is generated via feed forward neural networks (FFNN). The proposed control law utilizes some states of the system, which are estimated via the use of a high gain differentiator and a famous flatness property of nonlinear systems. This synthetic control strategy is named neuro-adaptive arbitrary order sliding mode control (NAAOSMC). The overall closed-loop stability is discussed in detail and simulations are carried out in Simulink environment of MATLAB to endorse effectiveness of the developed synthetic control strategy. Finally, comparison of the developed controller with the backstepping controller is done, which ensures the performance in terms of maximum power extraction, steady-state error and more robustness against sudden variations in atmospheric conditions.