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Currently, renewable power plants based on photovoltaic farms are considered as main sources of energy production which have been rapidly growing. However, changes in weather conditions are one of the issues facing this energy conversion system to provide the required power for the consumer. An efficient controller can appropriately control and improve the dynamic performance of the island microgrid based on the photovoltaic system. In this paper, a perturbation and observation method based on optimal fuzzy control is proposed to provide the required energy for the microgrid. In this regard, partial changes in the proportional and integral constants during the climate changes are calculated to ensure the convergence at the desired point. In order to find the desired parameters of the fuzzy system membership functions, a non-dominated sorting genetic algorithm is used. Then, the optimal duty cycle signal is injected into the boost converter. To verify and validate the performance of the proposed controller, a comparison is also made with the conventional observation and perturbation strategy. Also, different radiation conditions are considered for the under study photovoltaic system. Modeling of photovoltaic system and proposed control system has been performed by MATLAB / Simulink software. Finally, the simulation results show that the speed and accuracy of the maximum power point tracking by the proposed control system has been significantly improved.