This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time) internal state–space representation (a finite chain of integrators) of the fault vector. Next, a nonlinear state observer is designed based on the known parts of the augmented dynamics. This nonlinear filter (observer) reconstructs the fault signal as well as the states of the augmented system. We provide sufficient conditions that guarantee stability of the estimation error dynamics: firstly, asymptotic stability (i.e., exact fault estimation) in the absence of perturbations induced by the fault model mismatch (mismatch between internal ultra-local model for the fault and the actual fault dynamics), uncertainty, external disturbances, and measurement noise and, secondly, Input-to-State Stability (ISS) of the estimation error dynamics is guaranteed in the presence of these perturbations. In addition, to support performance-based estimator design, we provide Linear Matrix Inequality (LMI) conditions for L2-gain and L2−L∞ induced norm and cast the synthesis of the estimator gains as a semi-definite program where the effect of model mismatch and external disturbances on the fault estimation error is minimized in the sense of L2-gain, for an acceptable L2−L∞ induced norm with respect to measurement noise. The latter result facilitates a design that explicitly addresses the performance trade-off between noise sensitivity and robustness against model mismatch and external disturbances. Finally, numerical results for a benchmark system illustrate the performance of the proposed methodologies.

中文翻译：

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非线性系统的鲁棒故障估计器：超局部模型设计


本文提出了一个非线性估计器，用于对一类不确定非线性系统的过程和传感器故障进行稳健重建。所提出的故障估计方法通过故障向量的超局部（时间上）内部状态空间表示（有限的积分链）增强了系统动力学。接下来，基于增强动力学的已知部分设计非线性状态观测器。这个非线性滤波器（观察者）重建了故障信号以及增强系统的状态。我们提供了保证估计误差动力学稳定性的充分条件：首先，在没有由故障模型不匹配（故障的内部超局部模型与实际故障动力学之间的不匹配）、不确定性、外部干扰和测量噪声引起的扰动的情况下，渐近稳定性（即精确的故障估计），其次，在存在这些的情况下，保证估计误差动态的输入到状态稳定性 （ISS）扰动。此外，为了支持基于性能的估计器设计，我们为 L2-gain 和 L2-L∞ 诱导的范数提供了线性矩阵不等式 （LMI） 条件，并将估计器增益的综合转换为一个半定程序，其中模型失配和外部干扰对故障估计误差的影响在 L2-gain 的意义上最小化，对于可接受的 L2-L∞ 诱导的测量噪声范数。后一个结果有助于设计，明确解决噪声灵敏度和鲁棒性之间的性能权衡，以应对模型失配和外部干扰。最后，基准系统的数值结果说明了所提出的方法的性能。