Fault Tolerant Control for Non-Gaussian Stochastic Distribution Systems

A new fault tolerant control (FTC) problem via the output probability density functions (PDFs) for non-Gaussian stochastic distribution control systems (SDC) is investigated. The PDFs can be approximated by the radial basis functions (RBFs) of neural networks. Differently from the conventional FTC problems, the measured information is in the form of probability distributions of the system output rather than the actual output values. The control objective is to use the output PDFs to design control algorithm that can compensate the faults and attenuate the disturbances. As a result, the concerned FTC problem subject to dynamic relation between the input and output PDFs can be transformed into a nonlinear FTC problem subject to dynamic relation between the control input and the weights of the RBFs neural networks. Feasible criteria to compensate the faults and attenuate the disturbances are provided in terms of linear matrix inequality (LMI) techniques. In order to improve FTC performances, H ^∞ optimization techniques are applied to the FTC design problem to assure that the faults can be compensated and the disturbances can be attenuated. At last, an illustrated example is given to demonstrate the efficiency of the proposed algorithm, and the satisfactory results have been obtained.