Fault tolerant control based on stochastic distribution via RBF neural networks

Fault Tolerant Control for Non-Gaussian Stochastic Distribution Systems

“…Remark 1 Compared with the models considered in [3,10,19], there are the following several features: first of all, a radial basis function (RBF) neural network technique is proposed so that the PDF model is more practically reasonable; secondly, in the model adopted in [1], ω(y, u(t), F ) is omitted, which can lead to the conservative result.…”

“…So there is a need to further develop the FDD methods that can be applied to the stochastic systems subject to non-Gaussian distribution. Motivated by these factors, studies on stochastic distribution systems and stochastic distribution control have been investigated in [1,3,4,6,7,10,19,20,[22][23][24][25][31][32][33]. Differently from conventional FDD problems, the measurement information for the FDD is the output PDFs rather than the mean or variance of the output, and the stochastic variables involved in are not confined to the Gaussian ones.…”

Fault Detection and Diagnosis for Non-Gaussian Singular Stochastic Distribution Systems via Output PDFs

“…wherex(t) is the estimated state,Ŵ 1 is an estimated matrix In addition, similar to [7] and [16],In the rest of this paper, the following assumptions are needed. Assumption 1.…”

“…However, nonlinearity may lead to non-Gaussian output,where (especially for asymmetric distributions with multiple peaks) mean and variance of the system output are insufficient to characterize their statistical behavior precisely ( [11], [12], [13]). As such, there is need to further develop fault detection and diagnosis algorithms that can be applied to the stochastic system subjected to random parameter.On the other hand,along with the development of advance instruments and data processing technique, the measurements for feedback are the stochastic information which can be described by the probability density functions(PDFs) of the stochastic distribution system output rather than the actual output values.For such non-Gaussian stochastic system, we call stochastic distribution control(SDC) systems ( [3], [7], [10]- [16]). Different from any other previous stochastic control approaches,the stochastic variables are not confined to be Gaussian and the output PDFs of the stochastic system is concerned( [13]- [18]).…”

“…while the control objective of SDC systems is to control the shape of the output PDFs, the aim of FDD in SDC It is noted that if only output PDFs can be measured rather than the output vector itself,most existing observer-based FDD approaches are invalid. As a result, an observer-based fault detection and diagnosis approaches have been developed in reference( [3], [7], [11], [14], [15], [16],and reference therein) to detect and diagnose the fault in the non-Gaussian SDC system. However, concerning the FDD problem, few literatures have been reported to the singular non-gaussian stochastic distribution control systems.…”