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Solid oxide fuel cell (SOFC) is a promising energy conversion device with high efficiency, fuel flexibility and reduced emissions. An important tool in fuel cell development is mathematical modeling, which is particularly appropriate for SOFCs, where localized experimental measurements are difficult due to the high operating temperature. This chapter firstly reports static modeling studies of a SOFC using least squares support vector machine (LS-SVM) and genetic algorithm-radial basis function (GA-RBF) neural network, respectively. The development of control systems is an important technology issue in pursuing successful implementation of the SOFC. The results obtained from a good dynamic model can be very useful to guide future research of design, analysis and optimization of the SOFC. Furthermore, this dynamic model can also be used to develop a control system of the SOFC operation. So, an adaptive neural-fuzzy inference system (ANFIS) model and a Hammerstein model are established to describe the nonlinear dynamic properties of the SOFC separately. Finally, to protect the SOFC and meet the voltage demand of DC type loads, a model predictive control (MPC) is developed to control the output voltage of the SOFC. Simulation results demonstrate the potential of the established models and the excellence of the MPC controller.

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