Fault diagnostic filtering using stochastic distributions in nonlinear generalized H_∞ setting

A fault diagnosis problem is considered by using output probability density functions (PDFs) for stochastic time-delayed systems in the continuous time domain. For such systems, a B-spline approximation is used to model the output PDFs and the approximation coefficients (i.e., the weights) are then dynamically linked with the control input in the form of a weighting system. The modelling errors and system uncertainties resulting from both the B-spline expansion and the weighting system are merged into the system disturbances and the established weighting system is also subjected to nonlinearities, uncertainties and time delays. The generalized H_∞ optimization is applied to the fault diagnosis problem with the non-zero initial condition and the truncated norms. An LMI-based fault diagnostic filtering (FDF) method is presented such that the fault can be estimated and the disturbances can be attenuated. Simulations are given to demonstrate the efficiency of the proposed approach.