Considering the extensive applications of the model predictive control (MPC), this chapter investigates the MPC problem with an application to the optimal output consensus of high-order multi-agent systems. A synchronous distributed optimization algorithm for the MPC problem is proposed, and we further devise its asynchronous version. The algorithm allows agents to choose the uncoordinate step sizes depending on local information, which improves the flexibility of multi-agent systems. The convergence of the proposed algorithm is guaranteed if the positive uncoordinate step sizes satisfy the explicit conditions. Compared with the synchronous version that needs a global clock to control all agents for communication and update, the asynchronous algorithm does not require each agent in the multi-agent systems to update and communicate simultaneously, and also converges to the optimal global solution to the problem. The numerical simulations demonstrate the availability of the proposed algorithm and the validity of the theoretical results.