This paper addresses the problem of small fault detection for discrete-time nonlinear uncertain systems. The problem is challenging due to (i) the considered system is subject to unstructured nonlinear uncertain dynamics; and (ii) the faults are considered to be “small” in the sense that system states and control inputs in faulty mode remain close to those in normal mode. To overcome these challenges, a novel adaptive dynamics learning based fault detection scheme is proposed. Specifically, an adaptive dynamics learning approach is first proposed to achieve the locally-accurate approximation of the system uncertain dynamics. Then, based on the learned knowledge, a novel residual system is designed by using the absolute measures of the change of the system dynamics resulting from the fault effect. An adaptive threshold is developed based on the residual system for real-time decision making, i.e., the fault is claimed to be detected when the associated residual signal becomes larger than the adaptive threshold. Rigorous analysis is performed to deduce the small fault detectability condition, which is shown to be significantly relaxed compared to those of existing fault detection methods. Extensive simulations have also been conducted to demonstrate the effectiveness and advantages of the proposed approach.

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