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This paper presents a novel optimal neurocontroller that replaces the conventional controller (CONVC), which consists of the automatic voltage regulator and turbine governor, to control a synchronous generator in a power system using a multilayer perceptron neural network (MLPN) and a radial basis function neural network (RBFN). The heuristic dynamic programming (HDP) based on the adaptive critic design technique is used for the design of the neurocontroller. The performance of the MLPN-based HDP neurocontroller (MHDPC) is compared with the RBFN-based HDP neurocontroller (RHDPC) for small as well as large disturbances to a power system, and they are in turn compared with the CONVC. Simulation results are presented to show that the proposed neurocontrollers provide stable convergence with robustness, and the RHDPC outperforms the MHDPC and CONVC in terms of system damping and transient improvement.