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Based on a single-phase photovoltaic grid-connected inverter, a control strategy combining traditional proportional–integral–derivative (PID) control and a dynamic optimal control algorithm with a fuzzy neural network was proposed to improve the dynamic characteristics of grid-connected inverter systems effectively. A fuzzy inference rule was established after analyzing the proportional, integral, and differential coefficients of the PID controller. A fuzzy neural network was applied to adjust the parameters of the PID controller automatically. Accordingly, the proposed dynamic optimization algorithm was deduced in theory. The simulation and experimental results showed that the method was effective in making the system more robust to external disruption owing to its excellent steady-state adaptivity and self-learning ability. [ABSTRACT FROM AUTHOR]