基于LMI的参数随机变化系统的概率密度函数控制

针对模型参数在有界区域内随机变化的系统, 基于平方根 B 样条模型, 提出了输出概率密度函数 (Probability density function, PDF) 跟踪控制策略. 目标是控制系统输出的概率密度函数跟踪给定的概率密度函数. 通过 B 样条逼近建立了输出 PDF 和权值之间的对应关系, 把 PDF 的跟踪转化为权值的跟踪, 同时系统转化为 MIMO 系统,从而权值向量的跟踪就转化为 MIMO 系统的跟踪问题, 接着给出了系统输出概率密度函数跟踪给定概率密度函数的控制器存在的充分条件, 通过求解线性矩阵不等式完成状态反馈和输出反馈跟踪控制器的设计, 得到了系统具有 Hinfinity 范数界 Gamma 鲁棒镇定的结果. 仿真结果表明本文提出的控制算法是有效的.     

熵在随机系统故障诊断和容错控制中的应用

长期以来,关于随机动态系统的故障诊断和容错控制的研究一直是控制理论和应用的重要领域之一.随机控制系统故障诊断的目标是建立有效的故障估计算法以使残差信号方差最小这种方法仅适用于高斯型残差或者具有对称分布的概率密度函数的残差.然而,对非高斯残差而言,仅使用残差信号的方差不能够全面表示残差的不确定性.针对非高斯随机动态控制系...     

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。     

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。     

基于泡沫尺寸随机分布的铜粗选药剂量控制

为了稳定铜粗选选矿指标,提高矿产资源的利用水平, 根据铜粗选过程中泡沫尺寸分布随药剂量改变而动态变化的特点, 提出一种基于泡沫尺寸随机分布的铜粗选过程药剂量控制方法.首先, 针对泡沫尺寸分布具有非高斯统计特性, 基于方差和均值的统计参量难以表征该分布形态变化的问题, 提出了B样条估计方法以描述泡沫尺寸的概率密度函数(Probability density function, PDF); 然后, 针对B 样条权值相互关联的特点, 建立多输出最小二乘支持向量机模型(Multi-output least square support vector machine, MLS-SVM)以表征权值和药剂量的动态关系; 最后, 为减少系统的随机性, 采用基于熵的优化算法以确定药剂量, 实现对给定泡沫尺寸分布的跟踪控制.工业数据仿真验证了所提方法的有效性, 能有效稳定铜粗浮选的生产指标.     

随机激励下非线性水轮机系统的控制设计

针对一类随机非线性哈密顿系统提出了一种全新的反馈跟踪控制方法.该控制策略可以准确地控制系统输出的概率密度分布特性.闭环系统的稳定性也通过李雅普诺夫函数法得到严格的数学证明.最后,以随机非线性水轮机系统为例,详细演示了控制设计过程及其有效性.仿真结果表明,新的反馈控制策略可以使水轮机系统的输出满足预先指定的平稳概率密度函数.     

非高斯随机粗糙表面计算机仿真的研究

在摩擦学、光学等工程领域中,对于表面粗糙度的研究,总是以生成的随机粗糙表面为研究对象,且大多数研究都是建立在高斯随机表面的基础上,而实际的工程表面大多是非高斯随机表面.为此提出了一种基于快速傅里叶变换(FFT)、Johnson转换系统和自相关函数等理论仿真生成非高斯随机粗糙表面的方法,它可以生成具有给定偏斜度和峰度的随机粗糙表面.为了说明该方法的可行性和正确性,给出了不同偏斜度、峰度和自相关长度下的计算机仿真结果.结果表明:在一定的条件下用该方法仿真生成的非高斯随机粗糙表面,其输入的随机表面的统计参数与输出的统计参数吻合较好.     

一类仿射非线性系统的概率密度函数形状控制

针对一类仿射非线性有界动态随机系统,提出一种最优概率密度函数（PDF）跟踪控制算法,使得系统的输出PDF跟踪给定的PDF．首先利用线性B样条解耦得到仿射非线性状态方程和PDF逼近方程,使PDF跟踪转化为状态方程输出权值的跟踪;然后采用线性时变序列逼近方法将非线性系统转化为线性时变系统,通过对线性系统的迭代运算得到非线性系统的最优跟踪控制器,从而实现最优PDF跟踪．理论分析和仿真实验均表明了所提出算法的有效性．     

阈值阵列模型下的超阈值随机共振信噪比增益

研究了阈值阵列模型和超阈值随机共振现象.对该模型进行剖析,认为阈值阵列系统可以分解为单个阈值系统与集总平均器的级联.为了研究周期输入下的超阈值随机共振现象,理论分析了周期输入下的阈值阵列模型输出随机过程的统计特性,以输出信噪比增益作为随机共振的测度,固定输入信噪比,观测输出信噪比增益相对于阈值噪声方差的变化规律.证实当输入噪声为高斯噪声时,在阈值阵列系统中加入统计独立的高斯白噪声可使输出信噪比增益大于1,当输入噪声为非高斯噪声时,可获得更高的输出信噪比增益.     

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.     

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. Conver- gency analysis is performed for the error dynamic system raised from robust fault detection and fault diagnosis phase. Computer simulations are given to demon- strate the effectiveness of the proposed algorithm.     

Fault diagnosis and fault tolerant control for non-Gaussian time-delayed singular stochastic distribution systems

Stochastic distribution control (SDC) is a new branch of stochastic system control that the system output is the probability density function (PDF) of the output. In practice, some algebraic relations exist between the input and the weights of SDC systems, leading to a singular state space model between the weights and the control input which increases the complexity of the system. The ignorance of time delay in practical systems will make the effectiveness of the fault diagnosis (FD) and fault tolerant control (FTC) be reduced. In this paper, the linear B-spline basis functions are used to approximate the output PDF. A FD approach based on the adaptive observer is established to diagnose the size of fault in the singular time-delayed SDC system. With the fault diagnosis information, a fault tolerant controller based on PI tracking control scheme is constructed to make the post-fault PDF still track the given distribution. The post-fault closed-loop stability analysis with the practical fault tolerant controller is carried out based on the Lyapunov stability theorem. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed approach.     

Design of new fault diagnosis and fault tolerant control scheme for non-Gaussian singular stochastic distribution systems

New fault diagnosis (FD) and fault tolerant control (FTC) algorithms for non-Gaussian singular stochastic distribution control (SDC) systems are presented 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 the FD and FTC design. The proposed approach relies on an iterative learning observer (ILO) for fault estimation. The fault may be constant, fast-varying or slow-varying. Based on the estimated fault information, the fault tolerant controller can be designed to make the post-fault probability density function (PDF) still track the given distribution. Simulations are given to show the effectiveness of the proposed FD and FTC algorithms.     

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

In 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.     

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.     

Fault diagnosis and fault-tolerant control for non-Gaussian nonlinear stochastic systems via entropy optimisation

ABSTRACT

In this paper, the fault diagnosis (FD) and fault tolerant control (FTC) problems are studied for non-linear stochastic systems with non-Gaussian disturbance and fault. Unlike classical FD algorithms, the minimum entropy FD is adopted to minimise the residual entropy and control the shape of the probability density function (PDF) of the residual signal. The observation error system can be proved to be locally and ultimately bounded in the mean square sense. Since entropy can be used to characteriSe the uncertainty of the tracking error for non-Gaussian stochastic systems, the FTC controller is obtained by minimising the performance function with regard to the entropy of the tracking error in this paper. The PDF of the output tracking error is approximated by the B-spline model. An illustrative example is utilised to demonstrate the effectiveness of the FD and FTC algorithm, and satisfactory results have been obtained.     

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.     

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.     

Bumpless switching control for switched systems with partial actuator failures

This study is concerned with the bumpless transfer problem for switched systems with partial actuator failures, in order to obtain smooth system performance output transition. Taking into account that the system requires a controller switching from current sub-controller to a fault-tolerant sub-controller after actuator fault. And bumpless transfer for control input cannot be traditionally designed when the actuator fault occurs, while performance smoothing can be considered and it is actually the ultimate goal of bumpless transfer. Specifically, the actuator fault model is firstly established and partial actuator fault is considered. Then, the system performance output signal is deemed as the main design variable of bumpless transfer, and closed-loop control systems both previous and after controller switching are constructed. Moreover, by using model matching thought and the adaptive sliding mode control technique, a bumpless transfer compensator design strategy is given to drive the performance output variable (after controller switching) to track the one of reference model. At last, simulation results of numeric and application examples demonstrate the effectiveness of the proposed bumpless transfer strategy.