Small fault detection from discrete-time closed-loop control using fault dynamics residuals

Abstract This paper addresses the problem of small fault detection from closed-loop control for discrete-time nonlinear uncertain systems. The problem is challenging due to (i) the considered system is subject to unstructured nonlinear uncertain dynamics; (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; and (iii) fault detection needs to be accomplished during closed-loop control which might counteract the fault effects and thus diminish fault information for detection use. To overcome these challenges, a novel adaptive dynamics learning based fault detection scheme is proposed. Specifically, a new concept of fault dynamics residual is first developed to extract and represent enhanced fault information from closed-loop control. Then, an ideal estimator is constructed by using absolute measures of the proposed fault dynamics residuals. To make the ideal estimator implementable for systems with nonlinear uncertain dynamics, an adaptive dynamics learning approach is subsequently proposed to achieve the locally-accurate approximation of the uncertain fault dynamics. Finally, an adaptive threshold is developed based on the actual estimation 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.