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This paper describes a design of model predictive control for vehicle formation. The design can be model-based or data-based. In the model-based version, the controllers are designed from known models of the vehicles, whereas in the data-based version, the controller gains are computed directly from the vehicle input-output data, bypassing the predictive model identification step. The data-based version can be implemented adaptively to handle unexpected obstacles and changing operating environment. Simulation results illustrate how the theory can be applied to a group of vehicles to make them move in formation while tracking a moving target and avoiding obstacles.