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In this paper a novel fault diagnosis (FD) approach combing the rein-forcement learning (RL) and the deterministic learning theory (DLT)is proposed for a class of discrete-time nonlinear system with unknowndynamics. First, a bank of DLT-based dynamical neural network (NN)identifiers are utilized to achieve locally-accurate approximations ofthe unknown system dynamics along the normal and fault trajecto-ries. Based on this, a novel feature learning method combing the RLwith DLT is proposed to further adapt the NN weights to extract dis-criminative features. The extracted features are represented by constant NNs. Finally, constant NN-based dynamical estimators are constructedto achieve rapid FD. The novelties of the proposed methods are: 1)according to the DLT, the exponential convergence of the NN weightscan be rigorously analysed based on the Lyapunov stability theory;2) a new class of strategic utility function is designed based on theconcept of the synchronization error in DLT-based dynamical pat-tern recognition approach, which is different from other RL-based FDtechniques that penalise the future wrong FD decisions. Simulationresults shows the practical significance of the proposed FD method.