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

The 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.     

Model reference adaptive control of the output stochastic distributions for unknown linear stochastic systems

This paper presents a model reference based adaptive control approach for the control of the output probability density function for unknown linear time-invariant stochastic systems. Different from most existing models used in stochastic control, it is assumed here that the measured control input directly affects the distribution of the system output in probability sense. As such, the purpose of control is to make the shape of the probability density function of the system output as close as possible to a prespecified one. Using the weighted integration of the measurable output probability density functions, two adaptive on-line updating rules are developed which guarantee the global stability for theclosed loop adaptive control system under certain conditions. Ithas been shown, when there is no external disturbance, that the so-formed closed loop system also realizes the perfect tracking (i.e., the probability density function of the system output approaches a class of given distributions asymptotically). A simulated example is included to illustrate the use of the developed control algorithm and desired results have been obtained.     

随机分布系统状态记忆保性能控制的研究

对于连续随机分布控制中的保守性问题,采用平方根B样条逼近建立系统静态模型（输出概率密度函数模型）,利用系统输入和输出概率密度函数权值之间的动态关系建立动态模型,提出状态记忆反馈保性能控制算法,并利用凸优化技术优化算法,通过计算机仿真验证,该算法能够实现系统输出概率密度函数追踪目标概率密度函数,并满足规定的性能指标。     

Third-order cumulants based methods for continuous-time errors-in-variables model identification

In this paper, the problem of identifying stochastic linear continuous-time systems from noisy input/output data is addressed. The input of the system is assumed to have a skewed probability density function, whereas the noises contaminating the data are assumed to be symmetrically distributed. The third-order cumulants of the input/output data are then (asymptotically) insensitive to the noises, that can be coloured and/or mutually correlated. Using this noise-cancellation property two computationally simple estimators are proposed. The usefulness of the proposed algorithms is assessed through a numerical simulation.     

Stochastic Distribution Control of Singular Systems: Output PDF Shaping

This paper presents a new algorithm designed to control the shape of the output probability density function (PDF) of singular systems subjected to non-Gaussian input. The aim is to select a control input uk such that the output PDF is made as close as possible to a given PDF. Based on the B-spline neural network approximation of the output PDF, the control algorithm is formulated by extending the developed PDF control strategies of non-singular systems to singular systems. It has been shown that under certain conditions the stability of the closed-loop system can be guaranteed. Simulation examples are given to show the effectiveness of the proposed control algorithm.     

Linearized controller design for the output probability density functions of non-Gaussian stochastic systems

1 Introduction There are many practical systems that require the control of the shape of the output probability den- sity function rather than just their mean values and variances. These systems are seen in papermaking processes[1,2], chemical engineering, material science, combustion ?ame distribution systems and food pro- cessing industries. For example, in chemical engineer- ing the control of particle size distribution has al- ways been regarded as an important area of research[3], whilst …     

基于有理平方根逼近的非高斯随机分布系统的故障诊断和容错控制

随机分布系统指的是输入为常规向量而输出为系统输出的概率密度函数所描述的一类随机系统．该类系统控制算法的目标是选择一个控制输入使得系统的实际输出概率密度函数尽可能跟踪一个事先给定的概率密度函数．本文对采用有理平方根B样条逼近其输出概率密度函数的非高斯动态随机分布系统,提出了一种基于非线性自适应观测器的故障诊断方法．该方法可快速有效地诊断出非高斯随机分布系统故障．通过对故障系统的重组,使故障后系统的输出概率密度函数仍能跟踪给定的分布,实现了该随机系统的容错控制,提高了随机系统的可靠性．     

输出概率密度函数鲁棒弹性最优跟踪控制

研究了一类随机动态系统的鲁棒弹性最优跟踪控制问题。在采用B样条神经网络模型逼近随机动态系统的输出概率密度函数(PDF)的基础上,同时考虑系统模型和控制器增益不确定性,结合Lyapunov稳定性理论和线性矩阵不等式(LMI)技术,引入增广控制作用,设计基于广义状态反馈的鲁棒弹性最优跟踪控制器,目的是使系统的输出PDF跟踪给定PDF。通过求解LMI,所得控制器不仅能实现跟踪目的,而且能确保该随机动态系统全局稳定并满足一定的线性二次型性能指标上界。仿真结果表明该方法简单易行,且无需任何设计参数调整。     

Applying observer based FDI techniques to detect faults in dynamic and bounded stochastic distributions

This paper presents novel approach on applying the standard observer based fault detection technique to the change detection of the output probability density functions for dynamic stochastic systems. For such systems, the control inputs of the system appear as a set of variables in the probability density functions of the system output, and these variables affect the shape of the probability density function of the system output. Using the B-splines approximation theory, the measured probability density functions of the system output are represented by a set of weights which are functions of the control inputs to the system. This leads to a unique expression of the dynamic characteristics of the output probability density functions for the system. Using this expression, it has been shown that standard observer based fault detection technique can be used to detect any unexpected changes caused by the additive type of fault in the dynamic part of the system. In specific, two observers are constructed for the fault detection purposes, where the first observer is based on the linear weighted integration of the output probability density functions whilst the second observer uses the non-linear residual signal generated from the integration of the output probability density functions. In both cases, the convergence of the observers have been proved under certain conditions when there is no fault in the system. An applicability study to the detection of unexpected changes of particle size (i.e. flocculation size) in paper-making is included to demonstrate the use of the proposed algorithm and desired results have been obtained.     

Nonsymmetric PDF estimation by artificial neurons: application to statistical characterization of reinforced composites

We present a generalized adaptive activation function neuron structure which learns through an information-theoretic-based principle, which is able to estimate the probability density function of incoming input. It provides a low-order smooth robust estimate of the input signal probability density function. The presented method has been developed with reference to statistical characterization of polypropylene composites reinforced with vegetal fibers, that the proposed numerical experiments pertain to.     

Additive Fuzzy Systems: From Generalized Mixtures to Rule Continua

A generalized probability mixture density governs an additive fuzzy system. The fuzzy system's if‐then rules correspond to the mixed probability densities. An additive fuzzy system computes an output by adding its fired rules and then averaging the result. The mixture's convex structure yields Bayes theorems that give the probability of which rules fired or which combined fuzzy systems fired for a given input and output. The convex structure also results in new moment theorems and learning laws and new ways to both approximate functions and exactly represent them. The additive fuzzy system itself is just the first conditional moment of the generalized mixture density. The output is a convex combination of the centroids of the fired then‐part sets. The mixture's second moment defines the fuzzy system's conditional variance. It describes the inherent uncertainty in the fuzzy system's output due to rule interpolation. The mixture structure gives a natural way to combine fuzzy systems because mixing mixtures yields a new mixture. A separation theorem shows how fuzzy approximators combine with exact Watkins‐based two‐rule function representations in a higher‐level convex sum of the combined systems. Two mixed Gaussian densities with appropriate Watkins coefficients define a generalized mixture density such that the fuzzy system's output equals any given real‐valued function if the function is bounded and not constant. Statistical hill‐climbing algorithms can learn the generalized mixture from sample data. The mixture structure also extends finite rule bases to continuum‐many rules. Finite fuzzy systems suffer from exponential rule explosion because each input fires all their graph‐cover rules. The continuum system fires only a special random sample of rules based on Monte Carlo sampling from the system's mixture. Users can program the system by changing its wave‐like meta‐rules based on the location and shape of the mixed densities in the mixture. Such meta‐rules can help mitigate rule explosion. The meta‐rules grow only linearly with the number of mixed densities even though the underlying fuzzy if‐then rules can have high‐dimensional if‐part and then‐part fuzzy sets.     

Optimal probability density function control for NARMAX stochastic systems

This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output probability density function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.     

非高斯噪声下输出残差或状态估计误差的熵研究

基于非Gaussian噪声线性定常控制系统,通过控制滤波器输出残差或状态估计误差的条件概率密度函数形状来建立有效的滤波设计算法,创建滤波器输出残差或状态估计误差的条件概率密度函数的统一表现形式。利用复合概率密度函数的关系对残差或状态估计误差的条件概率密度函数的近似来实现非高斯残差的高斯化或相应的熵最小化。     

输出概率密度函数的最优跟踪控制:均方根B - 样条模型

在分析均方根B样条模型在实现输出概率密度函数最优跟踪控制时存在的问题的基础上,提出了将最优跟踪控制转化为非线性状态约束下的跟踪误差最优调节器,然后依据非线性状态约束和系统模型的特点分别设计了鲁棒变结构控制器及非线性观测器,并利用误差补偿控制来保证非线性观测器误差的有界性.仿真结果表明了提出的转换控制策略的有效性.     

Global robust output regulation of multivariable systems with nonlinear exosystem

It is well known that multi‐input, multi‐output nature of nonlinear system and generalized exosystem have posed some challenges to output regulation theory. Recently, the global robust output regulation problem for a class of multivariable nonlinear system subject to a linear neutrally stable exosystem has been studied. It has been shown that a linear internal model‐based state feedback control law can lead to the solution of previous problem. In this paper, we will further study the global robust output regulation problem of the system subject to a nonlinear exosystem. By utilizing nonlinear internal model design and decomposing the multi‐input control problem into several single‐input control problems, we will solve the problem by recursive control law design. The theoretical result is applied to the non‐harmonic load torque disturbance rejection problem of a surface‐mounted permanent magnet synchronous motor. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamical behavior of autoassociative memory performing noveltyfiltering for signal enhancement

This paper deals with the dynamical behavior, in probabilistic sense, of a simple perceptron network with sigmoidal output units performing autoassociation for novelty filtering. Networks of retinotopic topology having a one-to-one correspondence between input and output units can be readily trained using the delta learning rule, to perform autoassociative mappings. A novelty filter is obtained by subtracting the network output from the input vector. Then the presentation of a "familiar" pattern tends to evoke a null response; but any anomalous component is enhanced. Such a behavior exhibits a promising feature for enhancement of weak signals in additive noise. This paper shows that the probability density function of the weight converges to Gaussian when the input time series is statistically characterized by nonsymmetrical probability density functions. It is shown that the probability density function of the weight satisfies the Fokker-Planck equation. By solving the Fokker-Planck equation, it is found that the weight is Gaussian distributed with time dependent mean and variance.     

Deterministic and stochastic model based run-to-run control for batch processes with measurement delays of uncertain duration

A novel run-to-run control algorithm integrating deterministic and stochastic model based control is developed for batch processes with measurement delays of uncertain duration. This control algorithm is referred to as deterministic and stochastic model based control (DSMBC). The deterministic component responds quickly to deterministic changes while the stochastic component minimizes the effects arising from measurement delays of uncertain duration. The deterministic component uses a linear process model with parameters that are updated online. The stochastic component uses an error probability density function (PDF) to characterize the effects due to measurement delays and this error PDF is determined from deviations between the set-point and the available process output. To integrate the two control algorithms, the control input is determined by minimizing the weighted sum of the predicted error from the deterministic model and the information entropy of the error probability density distribution. Using a simulated setting where the rate of chemical vapor deposition is controlled, the performance of the proposed DSMBC is shown to be superior to that of EWMA.     

ITERATIVE LEARNING CONTROL IN FEEDBACK SYSTEMS BASED ON AN OBJECTIVE FUNCTION

An objective function is proposed and an iterative learning control algorithm is derived based on this. The objective function is a quadratic form consisting of the output error and the input. By adjusting the weights in the objective function, the control objective of good command following at smaller input energy can be realized. The weight on the input energy in the objective function is shown to be directly related to the forgetting factor for robust iterative learning control. The convergence of the control algorithm has been proven and its characteristics are shown in the simulation examples.