Abstract
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.
Highlights
In the past three decades, the research on design of controllers for stochastic systems has been regarded as an important aspect in control theory and practice
To improve the performance of the fault tolerant control (FTC) for the non-Gaussian stochastic distribution control systems, the proportional integral derivative (PID) controller and H ∞ optimization techniques are introduced in the presence of both the fault and the system disturbance, the control objective being to use the system output information (PDFs) to construct controller that can attenuate the disturbance and compensate the fault
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 probability density functions (PDFs) 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
Summary
In the past three decades, the research on design of controllers for stochastic systems has been regarded as an important aspect in control theory and practice. There is a need to further develop the FDD methods that can be applied to the stochastic systems subject to non-Gaussian distribution. Compared with the FDD, the virtual problem is to use the measured output PDFs to provide FTC strategies for non-Gaussian stochastic distribution control systems. There is a need to develop the FTC methods that can be applied to the non-Gaussian stochastic distribution control. To improve the performance of the FTC for the non-Gaussian stochastic distribution control systems, the proportional integral derivative (PID) controller and H ∞ optimization techniques are introduced in the presence of both the fault and the system disturbance, the control objective being to use the system output information (PDFs) to construct controller that can attenuate the disturbance and compensate the fault.
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