This paper presents a novel nonlinear control approach for the DC-DC bidirectional converter to efficiently operate the battery energy storage systems in DC micro-grids. The control design is based on sliding model back-stepping nonlinear control approach. This paper also proposes a novel equivalent dynamic model for the micro-grid system to verify the effectiveness of the proposed control system. The stability analysis is assessed using the Lyapunov stability theory. The effectiveness and robustness of the proposed method are evaluated through the simulation study and considering the nominal case, parameter uncertainties/variations, and sensor faults scenarios.