Fault detection and diagnosis for general discrete-time stochastic systems using output probability density estimation

A new approach of fault detection and diagnosis (FDD) for general stochastic systems in discrete-time is studied. Our work on this problem is motivated by the fact that most of the nonlinear control laws are implemented as digital controllers in reality. Different from the formulation of classical FDD problem, it is supposed that the measured information for the FDD is the probability density functions (PDFs) of the system output rather than its measured value. A radial basis function (RBF) neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighting of the RBFs neural network. Feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. An illustrated example is included to demonstrate the efficiency of the proposed algorithm, and satisfactory results are obtained.