We develop a multi-agent model predictive control method for a class of hybrid systems governed by discrete inputs and subject to global hard constraints. We assume that for each subsystem the local objective function is convex and the local constraint function is strictly increasing with respect to the local control variable. The proposed multi-agent control method is based on a distributed resource allocation coordination algorithm and it only requires limited information sharing among the local agents of the subsystems. Thanks to primal decomposition of the global constraints, the distributed algorithm can always guarantee global feasibility of the local control decisions, even in the case of premature termination. Moreover, since the control variables are discrete, a mechanism is developed to branch the overall solution space based on the outcome of the resource allocation coordination algorithm at each node of the search tree. Finally, the proposed multi-agent control method is applied to the charging control problem of electric vehicles under constrained grid conditions. This case study highlights the effectiveness of the proposed method.