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This work presents a novel design and development of a fuzzy predictive supervisory controller, based on genetic algorithms (GA), for gas turbines of combined cycle units. The control design is based on an objective function that represents the economic and regulatory performance of a gas turbine by using a dynamic optimal set-point for the regulatory level. A fuzzy model is considered in order to characterize the nonlinear behavior of the gas turbine, which is used in two supervisory control systems. The first fuzzy supervisory control design includes a fuzzy model, where its parameters are held constant for the successive predictions. For the second fuzzy supervisory control design, its parameters are updated in each prediction and its nonlinear optimization problem is solved using GAs. The proposed fuzzy supervisory controllers are compared against a supervisory controller based on linear models and a regulatory controller with constant optimal set-points. Results indicate that the fuzzy GA predictive supervisory controller captures adequately the nonlinearities of the process, which, in turn, provides a promising approach to improve the performance of the combined cycle unit.