Stochastic Distribution Control Systems Research Articles

States estimation and resilient control for non-Gaussian stochastic distribution control system under sensor attacks

This paper studies states estimation and resilient control schemes based on model predictive control (MPC) algorithm for a class of Takagi–Sugeno (T–S) fuzzy stochastic distribution control (SDC) system subjected to sparse sensor attacks. Firstly, a T–S fuzzy model is used to approximate the dynamics of a non-Gaussian SDC system, where the outputs of the system is the output probability density functions (PDFs). Secondly, in order to estimate the states and attacks in the system, a fuzzy Luenberger observer is designed. In addition, based on the estimated states and attacks, the designed MPC resilient control method achieves a satisfied tracking performance. Finally, the feasibility of the estimation algorithm and resilient controller are verified by simulation.

Fault‐tolerant control design for stochastic distribution control systems based on k‐step fault estimation

AbstractA novel scheme of fault‐tolerant control (FTC) and fault estimation (FE) for the stochastic distribution control (SDC) system with disturbance is investigated. The output probability density function (PDF) is modelled by the weight vector of the B‐spline neural network with the given basis function, and control of output probability density function can be converted to control of the weight vector of the B‐spline neural network. A k‐step fault estimation algorithm aiming at enhancing the accuracy of fault estimation is first applied to the stochastic distribution control system. Subsequently, a dynamic output feedback fault‐tolerant control algorithm is constructed by using the k‐step fault estimation information to guarantee that the target weight vector can be still approximated by the output weight vector in case of actuator fault. A simulation example is used to confirm the availability of the presented method.

Fault isolation and fault‐tolerant control for nonlinear stochastic distribution control systems with multiplicative faults

AbstractIn this paper, a fault isolation, diagnosis and fault tolerant control algorithm is proposed for nonlinear multiple multiplicative faults stochastic distribution control systems employing Takagi–Sugeno fuzzy system. To obtain the detailed fault information, a fault detection algorithm is introduced to discover the fault occurrence time. Then a fault isolation observer is built to produce the residual, and the error system is separated to subsystems affected only by disturbance and multiplicative faults. Moreover, a fault estimation scheme is presented to obtain the fault magnitude information. When faults occur, the system output probability density function will deviate from the desired distribution. So the model predictive control fault tolerant control scheme is needed to minimize the impact of faults as much as possible to make sure that the post fault output probability density function track the desired probability density function. The validity of the designed algorithm is demonstrated through a simulation example, where the fault tolerant control algorithm ensures that the system output probability density function still track the given output probability density function despite the complex case of multiple multiplicative faults occurring simultaneously.

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

AbstractComplex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non‐Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data‐driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision‐making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.

Fault diagnosis and fault-tolerant control for T-S fuzzy time-varying delay stochastic distribution systems with actuator and sensor faults

ABSTRACT The problem of fault diagnosis (FD) and fault-tolerant control (FTC) for a class of nonlinear time-varying delay stochastic distribution control (SDC) systems with actuator and sensor faults is investigated in this paper. The Takagi–Sugeno (T-S) model is used to approximate the nonlinear dynamics. The B-spline function is used to approximate the output probability density function (PDF) of the system. According to the output equivalence principle and Laplace transformation, an augmented state vector is designed to solve the time-varying delay problem. An augmented state adaptive diagnosis observer is proposed to estimate the system state, actuator and sensor faults simultaneously. A new fault-tolerant control algorithm is designed based on the PI control strategy to compensate sensor fault and actuator faults simultaneously. The sensor fault is compensated through the information obtained by the observer. The PI controller can compensate for the influence of the actuator fault, and the output PDF of system can still track the desired PDF when fault occurs. Simulation results are provided to show the effectiveness of the proposed method.

Fault isolation and fault-tolerant control for Takagi-Sugeno fuzzy time-varying delay stochastic distribution systems

A fault isolation, estimation, and fault-tolerant control (FTC) scheme for nonlinear time-varying delay stochastic distribution control systems was presented in this paper. The Takagi-Sugeno fuzzy model was adopted to approach the nonlinear dynamics of time-varying delay systems. According to the output equivalence principle and Laplace transformation, an augmented state vector was given to solve the time-varying delay problem. When multiple actuator faults and interference occur simultaneously, fault detection, isolation and fault estimation was designed to obtained the fault information. To decouple faults and obtain the value and location information of the fault, the system was separated into two parts through the designed multiple conversion matrices, in which one subsystem was only affected by one actuator fault. This has simplified the design of fault isolation and estimation. A adaptive observer for fault estimation was given. Then, fault information such as the time, location, and size was determined. The observer gain matrices were calculated using linear matrix inequality (LMI). When a fault was detected and diagnosed, a FTC algorithm was devised using the proportional-integral control scheme to compensate the fault as much as possible. It has been shown that even if multiple faults actuator occurred simultaneously, the FTC controller still ensured the output probability density function of the system traced the desired probability density function when a fault occurred. Finally, the expected results were obtained through the simulation example, which confirmed the effectiveness of the method.

Fault Diagnosis and Fault Tolerant Control for T–S Fuzzy Stochastic Distribution Systems Subject to Sensor and Actuator Faults

The problem of fault diagnosis (FD) and fault tolerant control for a class of Takagi–Sugeno (T–S) fuzzy stochastic distribution control systems subject to sensor and actuator faults is discussed in this article. First, fuzzy logic models are used to approximate the output probability density function (PDF). Next, an adaptive augmented state/FD observer is proposed to estimate the system state, sensor and the actuator faults simultaneously. New expected weights based on the sensor fault estimation information and a PI-type fuzzy feedback fault tolerant controller are designed to compensate the effect of sensor fault and actuator fault simultaneously. When the sensor fault occurs, the expected objective is redesigned to compensate the sensor fault. Meanwhile, the PI controller can compensate the effect of actuator fault, and the output PDF of the system can still track the desired PDF after the fault occurs. Finally, an example of quality distribution control in chemical reaction process is given to confirm the effectiveness of the algorithm.

Discrete-Time 2-Order Sliding Mode Fault-Tolerant Tracking Control for Non-Gaussian Nonlinear Stochastic Distribution Control Systems with Missing Measurements

In this paper, a method of fault diagnosis (FD) and fault-tolerant tracking control (FTTC) is investigated for non-Gaussian nonlinear stochastic distribution control (SDC) systems with missing measurements. The phenomenon of the randomly occurring missing measurements is described as a Bernoulli process. The missing measurements during transmission are compensated with the data successfully transmitted at the previous moment. The residual signal of the fault diagnosis observer is different from that of the general system. Using the integral of the error of the output probability density function (PDF) as the driving information, the system state and fault can be estimated by an adaptive fault diagnosis observer. Then, a novel fault-tolerant tracking controller is designed based on a discrete-time 2-order sliding mode to make the post-fault PDF still track the target. Two simulated examples are included to illustrate the effectiveness of the theoretical results.

Sensor Fault Diagnosis and Fault-Tolerant Control for Non-Gaussian Stochastic Distribution Systems

A sensor fault diagnosis method based on learning observer is proposed for non-Gaussian stochastic distribution control (SDC) systems. First, the system is modeled, and the linear B-spline is used to approximate the probability density function (PDF) of the system output. Then a new state variable is introduced, and the original system is transformed to an augmentation system. The observer is designed for the augmented system to estimate the fault. The observer gain and unknown parameters can be obtained by solving the linear matrix inequality (LMI). The fault influence can be compensated by the fault estimation information to achieve fault-tolerant control. Sliding mode control is used to make the PDF of the system output to track the desired distribution. MATLAB is used to verify the fault diagnosis and fault-tolerant control results.

Fault Tolerant Control for Nonlinear Singular Stochastic Distribution Systems Based on Fuzzy Modeling

When the desired output probability density function (PDF) is unknown, the active fault-tolerant control (FTC) method for the non-Gaussian nonlinear singular stochastic distribution control (SDC) system is investigated in this paper. Algebraic constraints and the nonlinearity in singular systems make the design of fault diagnosis and fault-tolerant control more complex. Different from traditional static modeling methods, the linear fuzzy logic system is served for approximating the output PDF. Takagi-Sugeno (T-S) fuzzy model is used to describe the nonlinear system. Subsequently, a fuzzy descriptor fault diagnosis (FD) observer is used to provide the unknown fault information for the fault-tolerant controller design. Combining minimum entropy control and fault compensation algorithm, the minimum Shannon entropy fault tolerant control strategy is developed to compensate the performance losses caused by the fault. At last, simulation results are applied to demonstrate the effectiveness of the proposed algorithms.

Minimum rational entropy fault tolerant control for non-Gaussian singular stochastic distribution control systems using T-S fuzzy modelling

ABSTRACTIn this paper, a new fault diagnosis (FD) and fault tolerant control (FTC) algorithm for a non-Gaussian nonlinear singular stochastic distribution control (SDC) system is studied. The rational square-root fuzzy logic model is used to approximate the output probability density function of non-Gaussian processes and a Takagi-Sugeno (T-S) fuzzy model is employed to transform the non-Gaussian nonlinear SDC system into a fuzzy SDC system. An adaptive fuzzy fault diagnosis observer is constructed to achieve reconstruction of system state and fault. Based on the estimated fault information, the controller is reconfigured by minimising the performance index with regard to the rational entropy subjected to mean constraint. Minimum rational entropy fault tolerant control is introduced to make the output of the past-fault SDC system still have the minimum uncertainty. Simulation results are provided to demonstrate the validity of the FD and minimum rational entropy FTC algorithm.

Collaborative operational fault tolerant control for stochastic distribution control system

Based on a class of industrial processes, a new distributed fault diagnosis approach and a collaborative operational fault tolerant control law are proposed for an irreversible interconnected stochastic distribution control (SDC) system with boundary conditions. This control method is different from the existing collaborative fault tolerant controllers which enable the output probability density function (PDF) to track a desired PDF as close as possible. When fault occurs, a setpoint redesigned fault tolerant approach is adopted to accommodate the fault instead of reconstructing the controller. An augmented PID nominal controller and a setpoint compensation item with linear structure are used to obtain a collaborative operational fault tolerant controller via solution of linear matrix inequalities (LMIs). Simulations are included to show the effectiveness of the proposed algorithms where encouraging results have been obtained.

Fault diagnosis and fault tolerant control for the non-Gaussian nonlinear stochastic distribution control system using Takagi-Sugeno fuzzy model

For the non-Gaussian nonlinear stochastic distribution control system using Takagi-Sugeno fuzzy model, the nonlinear dynamic system is converted to a linear system. A fault diagnosis algorithm using RBF neural network and a sliding mode fault tolerant control algorithm is presented. A new adaptive fault diagnosis algorithm is adopted to diagnose the gradual fault that occurred in the system, and the stability of the observation error system is proved. Differential evolution (DE) algorithm is used to optimise the central vector and width vector of RBF neural network. The sliding mode control algorithm is used to reconfigure the controller, based on the fault estimation information. The post-fault probability density function (PDF) can still track the given distribution. Finally, simulation results show the effectiveness of the proposed fault diagnosis and fault tolerant control algorithm.

Fault diagnosis and fault tolerant control for the non-Gaussian nonlinear stochastic distribution control system using Takagi-Sugeno fuzzy model

For the non-Gaussian nonlinear stochastic distribution control system using Takagi-Sugeno fuzzy model, the nonlinear dynamic system is converted to a linear system. A fault diagnosis algorithm using RBF neural network and a sliding mode fault tolerant control algorithm is presented. A new adaptive fault diagnosis algorithm is adopted to diagnose the gradual fault that occurred in the system, and the stability of the observation error system is proved. Differential evolution (DE) algorithm is used to optimise the central vector and width vector of RBF neural network. The sliding mode control algorithm is used to reconfigure the controller, based on the fault estimation information. The post-fault probability density function (PDF) can still track the given distribution. Finally, simulation results show the effectiveness of the proposed fault diagnosis and fault tolerant control algorithm.

Fault diagnosis and model predictive tolerant control for non-Gaussian stochastic distribution control systems based on T-S fuzzy model

A Takagi-Sugeno (T-S) fuzzy model is applied to approximate the nonlinear dynamics of stochastic distribution control (SDC) systems, in which linear radial basis function (RBF) neural network is adopted to approximate the output probability density function (PDF) of non-Gaussian SDC systems. Considering the situation that fault may occur, a fuzzy adaptive fault diagnosis observer is designed to estimate the fault value. Besides, the Lyapunov stability theory is used to analyse the stability of the observation error system. Based on the fault estimation information and model predictive control (MPC) algorithm, the active fault tolerant control strategy is given. Finally, a simulation example is given to verify the effectiveness of the proposed control algorithm.

Minimum Entropy Active Fault Tolerant Control of the Non-Gaussian Stochastic Distribution System Subjected to Mean Constraint

Stochastic distribution control (SDC) systems are a group of systems where the outputs considered is the measured probability density function (PDF) of the system output whilst subjected to a normal crisp input. The purpose of the active fault tolerant control of such systems is to use the fault estimation information and other measured information to make the output PDF still track the given distribution when the objective PDF is known. However, if the target PDF is unavailable, the PDF tracking operation will be impossible. Minimum entropy control of the system output can be considered as an alternative strategy. The mean represents the center location of the stochastic variable, and it is reasonable that the minimum entropy fault tolerant controller can be designed subjected to mean constraint. In this paper, using the rational square-root B-spline model for the shape control of the system output probability density function (PDF), a nonlinear adaptive observer based fault diagnosis algorithm is proposed to diagnose the fault. Through the controller reconfiguration, the system entropy subjected to mean restriction can still be minimized when fault occurs. An illustrative example is utilized to demonstrate the use of the minimum entropy fault tolerant control algorithms.

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

This paper investigates the problem of fault detection and diagnosis (FDD) problem for non-gausian singulat stochastic distribution control (SDC) systems via the output probability density functions(PDFs). The PDFs can be approximated by using square-root B-spline expansion,via this expansions to represent the dynamics weighting systems between the system input and the weights related to the output PDFs. In this works ,an optimal fault detection and diagnosis algorith is present by introducing the parameter-updating .when the fault occurs, an adaptive network parameter-updating law is designed to approximated the fault. Finally, the simulation result are given to show that the approach can detect faults and estimate the size of fault.

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Robust fault diagnosis and fault‐tolerant control for non‐Gaussian uncertain stochastic distribution control systems

SummaryThe purpose of fault diagnosis of stochastic distribution control systems is to use the measured input and the system output probability density function to obtain the fault estimation information. A fault diagnosis and sliding mode fault‐tolerant control algorithms are proposed for non‐Gaussian uncertain stochastic distribution control systems with probability density function approximation error. The unknown input caused by model uncertainty can be considered as an exogenous disturbance, and the augmented observation error dynamic system is constructed using the thought of unknown input observer. Stability analysis is performed for the observation error dynamic system, and the H∞ performance is guaranteed. Based on the information of fault estimation and the desired output probability density function, the sliding mode fault‐tolerant controller is designed to make the post‐fault output probability density function still track the desired distribution. This method avoids the difficulties of design of fault diagnosis observer caused by the uncertain input, and fault diagnosis and fault‐tolerant control are integrated. Two different illustrated examples are given to demonstrate the effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.