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This paper uses the recently proposed H∞-learning method, for updating the parameter of the radial basis function neural network (RBFNN) used as a control scheme for the unified power flow controller (UPFC) to improve the transient stability performance of a multimachine power system. The RBFNN uses a single neuron architecture whose input is proportional to the difference in error and the updating of its parameters is carried via a proportional value of the error. Also, the coefficients of the difference of error, error, and auxiliary signal used for improving damping performance are depicted by a genetic algorithm. The performance of the newly designed controller is evaluated in a four-machine power system subjected to different types of disturbances. The newly designed single-neuron RBFNN-based UPFC exhibits better damping performance compared to the conventional PID as well as the extended Kalman filter (EKF) updating-based RBFNN scheme, making the unstable cases stable. Its simple architecture reduces the computational burden, thereby making it attractive for real-time implementation. Also, all the machines are being equipped with the conventional power system stabilizer (PSS) to study the coordinated effect of UPFC and PSS in the system.