Adaptive neuro-fuzzy inference system (ANFIS) technique is a significant alternative of research which is structured with a combination of two soft-computing strategies of fuzzy logic and artificial neural network. The design of ANFIS controller for a single-phase fullbridge inverter with pulse width modulation is demonstrated here in the presence of different disturbances. Moreover, an LC filter is designed to decrease the disturbing harmonics which the stability of the filter can be noted as an important issue. Based on the fuzzy C-mean clustering method used for decreasing fuzzy rules, the computational burden has been improved resulting in faster dynamic performance. This method considers the system as a black-box structure which omits the need for an exact model of system and can be an appropriate technique for ill-defined systems. Additionally, to deal with the variations of supply DC voltage, a fractional-order proportional-integral-derivative controller is designed which is tuned by particle swarm optimiser algorithm and can generate a sinusoidal reference for the system input. This double-loop control technique is known as cascade control strategy. It can be seen that ANFIS scheme provides appropriate results with less computational burden and simple structure with optimised responses in challenging conditions. The capability of the proposed method is validated for different operating conditions through simulation and experimental results.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.