Fault Identification Speed Analysis for a Class of Nonlinear Uncertain Systems Using High Gain Observer and Deterministic Learning

In this paper, we propose a novel approach for rapid fault identification (FI) in a class of nonlinear uncertain systems, with a particular emphasis on enhancing the speed of identification. By harnessing the high gain observer technique in tandem with deterministic learning, the proposed method effectively addresses unknown fault dynamics and unmeasurable states. A key contribution of this research is the development of a high gain observer that integrates learning to simultaneously estimate system states and identify faults, thus expediting the FI process. The method ensures satisfaction of a partial persistent excitation (PE) condition, leading to the input-to-state stability of the state and parameter estimation error system. We employ a Lyapunov function to scrutinize the relationship between the identification speed and the PE level of the neural networks. Our findings indicate that the partial PE condition allows the radial basis function (RBF) network to efficiently approximate unknown fault dynamics quickly. The efficiency and learning speed of the FI method are validated through comprehensive simulation studies.