Fault Detection for a Class of Nonlinear Systems in Presence of Unmodeled Dynamics and Parametric Uncertainties Using Adaptive Robust Observers

The goal of this work is to present some theoretical results which can be used for increasing fault sensitivity of a detection scheme, without sacrificing robustness. Robustness against modeling uncertainties and fault sensitivity are two contradicting demands, and typically, one is achieved at the expense of the other. The main reason for this trade-off is the use of a worst case scenario bound for modeling uncertainties at the residual evaluation stage. Many robust fault detection algorithms have been proposed based on the assumption that an a priori known functional bound exists for modeling uncertainties. In the present work, we look into the two main sources of modeling uncertainties, parametric uncertainties and unmodeled dynamics, and carefully examine their effect on residual evaluation. Finally, based on our analysis, and certain assumptions about the unmodeled dynamics and parametric uncertainties, we propose a threshold for residual generation and evaluation, and analytically prove its superior robustness and sensitivity properties.