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The configuration of a two-wheeled vehicle, such as a Segway, involves non-holonomic constraints, and thus it cannot be stabilized by continuous and time-invariant state feedback. Because of the nonlinear nature of the nonholonomic constraints, the realization of a model predictive control (MPC) algorithm for this class of vehicles is a difficult task. This paper proposes an MPC method that can achieve a long prediction horizon and has a short computation time. First, the optimization of an input (i.e., velocity and steering) sequence is formulated as a graph search problem by restricting the inputs to discrete values. Next, the optimized control result is learned by a machine learning method, such as support vector machine (SVM). Compared to nonlinear optimization, a longer horizon MPC can be realized. The advantages of the proposed method are demonstrated with simulation and experimental results.