Stochastic Distribution Control Research Articles

Robust fault diagnosis for non-Gaussian stochastic systems based on the rational square-root approximation model

The task of robust fault detection and diagnosis of stochastic distribution control (SDC) systems with uncertainties is to use the measured input and the system output PDFs to still obtain possible faults information of the system. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper, a robust nonlinear adaptive observer-based fault diagnosis algorithm is presented to diagnose the fault in the dynamic part of such systems with model uncertainties. When certain conditions are satisfied, the weight vector of the rational square-root B-spline model proves to be bounded. Convergency analysis is performed for the error dynamic system raised from robust fault detection and fault diagnosis phase. Computer simulations are given to demonstrate the effectiveness of the proposed algorithm.

Fault detection, diagnosis and tolerant control for non-Gaussian stochastic distribution systems using a rational square-root approximation model

Stochastic Distribution Control (SDC) systems are a group of systems where the outputs considered are the measured Probability Density Functions (PDFs) of the system output whilst subjected to a normal crisp input. The purpose of the control algorithm design of such systems is to choose a control input such that the PDF of the system output can follow a prespecified PDF as close as possible. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper a non-linear adaptive observer-based fault diagnosis algorithm is proposed to diagnose the fault in the dynamic part of such systems. Using the estimation to the unknown fault, a fault tolerant control via a controller reconfiguration is proposed, where it has been shown that a good output PDF tracking can still be realised when fault occurs in the system. A simulated example is given to illustrate the use of the proposed algorithm.

Lyapunov-based controller design for bounded dynamic stochastic distribution control

Following recent development in the modelling and control of the output probability density function of dynamic stochastic systems, a new approach for the controller design is presented using square root approximation, where a set of B-spline functions are used to approximate the square root of the measured output probability density function to guarantee its positiveness. A performance function is defined which measures the tracking error of the output probability density function with respect to a given distribution. Instead of finding an optimal control which minimises this performance function and then analysing the stability of the closed-loop system, the new approach directly uses the performance function as a Lyapunov function to design the required controller. As a result, the controller obtained not only guarantees the decreasing of the performance function with respect to time, but also stabilises the closed-loop system, realising an asymptotically tracking performance of the output probability density function with respect to its target distribution. The algorithm described has been tested on a simulated example and desired results have been achieved.