In this work, we propose a control strategy based on an iterative Linear Quadratic Regulator (iLQR) to solve a synchronization problem for interconnected systems in a distributed leader-follower context. This method is applied in a network of cart-pole agents where each of them is a nonlinear system with 4-dimension states and one input, used in mechanical systems. The proposed method solves an iLQR using its data and information from the neighborhood. A direct graph model for the communication network is worked to validate the proposed strategy. Finally, we tested the methodology in a numerical example with a homogeneous network where each agent reaches a synchronization.