This work presents a synchronization problem in a multiagent discrete system with an active leader solved through Model Predictive Control. Hence, a state estimation problem arises when only some of the agent's states are measurable, and we use the framework of Moving Horizon Estimation to formulate it. Since control and estimation problems are optimization-based, we introduce a method that solves both problems. This method proposes an algorithm based on the Alternating Direction Method of Multipliers (ADMM), where each agent only uses local information from its neighborhood. Finally, a numerical example shows the effectiveness of the proposed algorithm.