Controlling the domain wall (DW) trajectory in magnetic network structures is crucial for spin-based device related applications. The understanding of DW dynamics in network structures is also important for study of fundamental properties like observation of magnetic monopoles at room temperature in artificial spin ice lattice. The trajectory of DW in magnetic network structures has been shown to be chirality dependent. However, the DW chirality periodically oscillates as it propagates a distance longer than its fidelity length due to Walker breakdown phenomenon. This leads to a stochastic behavior in the DW propagation through the network structure. In this study, we show that the DW trajectory can be deterministically controlled in the magnetic network structures irrespective of its chirality by introducing a potential barrier. The DW propagation in the network structure is governed by the geometrically induced potential barrier and pinning strength against the propagation. This technique can be extended for controlling the trajectory of magnetic charge carriers in an artificial spin ice lattice.