基于最小信息损失准则的降阶LQG控制器设计

从信息论的角度出发,研究了LQG控制器降阶问题。在考察系统内部状态信息描述的基础上,提出了两种基于交叉格莱姆矩阵最小信息损失的LQG控制器降阶方法。将由这两种方法得出的降阶LQG控制器分别与全阶LQG控制器、基于最小K-L信息距离的降阶控制器进行仿真对比研究,比较各闭环系统的控制性能。仿真结果表明,提出的降阶控制器能较好地逼近全阶控制器实现闭环系统性能。     

张量积Bézier曲面降阶逼近的新方法

基于 L2 范数 ,给出基于曲面间体积极小的约束优化算法 ,将 Bézier曲面的降阶问题转变为线性方程组的求解 ,并给出降阶逼近问题解的存在性证明 .文中还对逼近误差进行了分析 ,并利用曲面离散算法减少降阶逼近误差     

基于交叉Gram矩阵的双侧H_2最优模型降阶方法

针对单输入单输出(SISO)线性时不变系统,提出了Grassmann流形上基于交叉Gram矩阵的双侧H2最优模型降阶方法。首先,将误差系统的H2范数通过交叉Gram矩阵表示,并且把它看成关于变换矩阵的代价函数。其次,引入Grassmann流形,将代价函数看作是定义在Grassmann流形上的非负实值函数。然后,在Grassmann流形上进行线性搜索,寻找使得代价函数尽可能小的一组变换矩阵。运用此方法对大规模SISO线性时不变系统进行降阶,可以得到精度较高的降阶系统。最后,数值算例验证了该算法的近似效果。     

电动助力转向系统多领域鲁棒控制模型的降阶方法

随着人们对汽车操纵舒适性、安全性和节能等方面要求的提高,鲁棒控制算法越来越广泛的应用于电动助力转向（EPS）控制系统中．针对高阶鲁棒控制器实时性差、成本高等问题,提出最优平方积分误差（ISE）模型降阶方法．应用该方法对EPS系统鲁棒控制器进行降阶,并与最优Hankel范数降阶法进行比较．仿真结果表明,最优ISE降阶方法具有更好的降阶效果,降阶系统具有很好的鲁棒性．     

L∞范数下使用基本曲线和修正曲线的带约束Bézier曲线降阶

为避免直接求解基于L∞距离的带约束逼近的非线性最优解引起的复杂性,提出了一种把降阶逼近曲线分解为基本曲线和修正曲线的降阶方法.基本曲线利用约束Legendre多项式可得到显式解,且保证降阶后曲线满足要求的边界插值条件;修正曲线的控制顶点由降阶逼近曲线和原曲线的差定义,能够在L∞范数意义下极小化降阶逼近曲线与原曲线的误差.文中方法以简单稳定的方式实现保端点插值的一次降多阶,并达到L∞范数意义下对原曲线的近似最佳逼近.最后通过实例说明了文中方法的有效性.     

K-power系统在Grassmann流形上的单侧模型降阶方法

K-power系统作为一类比较特殊的双线性系统,可以由一系列阶数相对较小的子系统构成,这使得K-power系统具有特殊的结构.K-power系统在Grassmann流形上的模型降阶方法将误差系统的H_2范数看作是定义在Grassmann流形上的代价函数,然后,沿测地线执行线性搜索寻找使得代价函数最小的变换矩阵.为了保持系统降阶前后结构的一致性,算法以K-power系统中各个子系统的变换矩阵为对角线元素构成双线性系统的变换矩阵.此外,算法有效地利用了K-power系统的结构特性,使得该算法在对K-power系统进行降阶时较一般的双线性系统的模型降阶方法有更少的计算量.     

几种模型降阶方法的仿真对比研究

算法比较研究,比较几种主要模型降阶方法的优缺点,为给工程应用提供方法参考.利用奇异值分解的模型降阶方法具有较好的理论性质,能够保持降阶系统结构特性,但计算成本较高故不适合大规模动态系统的降阶;采用矩匹配的模型降阶方法计算简便,适合大规模系统降阶,但无法保证降阶系统稳定性,也很难求得降阶误差界.最小二乘降阶法同时利用了系统的Gramian矩阵和Krylov子空间理论,结合了二者的优点,使得降阶过程计算简化,保持了降阶系统的结构特性,而且降阶误差进一步减小.仿真算例证明了最小二乘法较前两者具有优越性.     

基于Hankel范数模型降价的控制对象的名义模型选择

研究了控制对象具有多个模型时,求取其适合鲁棒控制器设计的名义模型的问题. 提出了一种基于Hankel范数模型降阶的名义模型选择算法.仿真结果确认了算法的有效 性.     

基于模型降阶的分数阶系统动态性能研究

由于大多数分数阶系统阶次过高,使得系统的控制器设计变得非常困难,会造成系统控制精度变差且动态性能降低等不利因素,而模型降阶技术是解决这一问题的有效工具.首先简要介绍了H2范数模型降阶的一般方法,并提出一种新的降阶模型结构,可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统.仿真结果证明,采用改进型H2范数模型降阶方法不仅保持了原有分数阶模型系统的动态性能而且还提升了原有整数阶模型系统的动态性能.     

阀控电液伺服压力脉冲实验自抗扰控制方法

针对压力脉冲疲劳测试系统在测试过程中工件体积的不确定性以及脉冲疲劳测试系统的机械与液压双动态耦合问题,首先,提出通过奇异值摄动理论将压力脉冲疲劳测试系统的多动态耦合进行解耦降阶;然后,利用自抗扰控制算法实现对系统模型降阶误差以及体积参数不确定性等干扰的补偿,保证测试系统输出的压力对指令信号的准确跟踪;最后,对基于降阶模型的自抗扰算法的稳定性和误差收敛性进行理论和定量分析,并对算法的可行性和有效性进行联合仿真和实验验证.研究结果表明,基于降阶模型的自抗扰控制算法对压力脉冲疲劳测试系统中工件体积参数的变化具有良好的鲁棒性且能够有效估计和补偿系统模型降阶误差等干扰,其跟踪性能相比于传统的PID控制器最大提升35.4%.     

基于最大化依赖的恐怖行为背景特征提取方法

针对恐怖数据集中存在的属性值残缺问题,提出了基于最大化背景向量与行为之间依赖关系的压缩背景空间(CCS)方法。该方法基于希尔伯特-施密特独立标准和希尔伯特-施密特范数,它们能有效检测变量间的关联性。CCS通过使得背景向量线性投影后的低维特征与行为之间希尔伯特-施密特范数最大化,从而实现背景向量与行为之间的依赖关系最大化,更好地发现两者之间的关联性,减小属性值残缺带来的影响。然后利用分类模型(如支持向量机(SVM))对所得到的低维特征进行学习(CCS+SVM),实现高效预测。在MAROB数据集上的实验表明:与SVM模型、基于传统特征提取方法(如PCA和CCA)的SVM模型以及已有的恐怖行为预测算法CONVEX相比,CCS+SVM的性能在查全率和F值上分别提高1.5%和1.0%以上,而查准率和ROC曲线下面积(AUC)值与最好性能相当。实验结果表明,CCS+SVM能够较好地解决恐怖数据集中的属性值残缺问题。     

Control configuration selection for bilinear systems via generalised Hankel interaction index array

Decentralised and partially decentralised control strategies are very popular in practice. To come up with a suitable decentralised or partially decentralised control structure, it is important to select the appropriate input and output pairs for control design. This procedure is called control configuration selection. It is well known that a suitable control configuration selection is an important prerequisite for a successful industrial control. In this paper the problem of control configuration selection for multiple-input and multiple-output (MIMO) bilinear processes is addressed. First, the concept of the cross-gramian is developed for bilinear systems. The conditions for the existence of generalised cross-gramian are derived. It is shown that if the cross-gramian exists it is the solution to the generalised Sylvester equation. To obtain the cross-gramian in a more computationally efficient way, an iterative method for solving the generalised Sylvester equation is proposed. The generalised cross-gramian is used to form the generalised Hankel interaction index array. The generalised Hankel interaction index array is used for control configuration selection of MIMO bilinear processes. Most of the results on control configuration selection, which have been proposed so far, can only support linear systems. The proposed method supports bilinear processes, takes the effects of dynamics of the process into account and can be used to propose a richer (sparse or block diagonal) controller structure. More importantly, since for each element of generalised Hankel interaction index array just one generalised Sylvester equation is needed to be solved, the proposed control configuration selection method is computationally more efficient than its gramian-based counterparts.     

Minimizing the Discrepancy Between Source and Target Domains by Learning Adapting Components简

Predicting the response variables of the target dataset is one of the main problems in machine learning. Predictive models are desired to perform satisfactorily in a broad range of target domains. However, that may not be plausible if there is a mismatch between the source and target domain distributions. The goal of domain adaptation algorithms is to solve this issue and deploy a model across different target domains. We propose a method based on kernel distribution embedding and Hilbert-Schmidt independence criterion （HSIC） to address this problem. The proposed method embeds both source and target data into a new feature space with two properties： 1） the distributions of the source and the target datasets are as close as possible in the new feature space, and 2） the important structural information of the data is preserved. The embedded data can be in lower dimensional space while preserving the aforementioned properties and therefore the method can be considered as a dimensionality reduction method as well. Our proposed method has a closed-form solution and the experimental results show that it works well in practice.     

Hankel norm approximation of linear systems with time-varying delay: continuous and discrete cases

This paper investigates the problem of Hankel norm model reduction for linear systems with time-varying delay in the state. For a given stable system, our attention is focused on the construction of reduced-order model, which guarantees the corresponding error system to be asymptotically stable and has a specified Hankel norm error performance. Two different approaches are proposed to solve this problem. One casts the model reduction into a convex optimization problem by using a linearization procedure, and the other is based on the cone complementarity linearization idea, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints. Both continuous and discrete time cases are considered. A numerical example is provided to show the effectiveness of the proposed theory.     

Frequency-weighted ℒ∞ norm and optimal Hankelnorm model reduction

A new relative error model reduction method is proposed using frequency-weighted balanced realization, and explicit ℒ_∞ norm error bounds are also derived for the relative error and multiplicative error. The method only needs to solve two Lyapunov equations. It is further shown that this method is equivalent to the balanced stochastic truncation if the plant is square and minimum phase. This paper also gives a complete solution to the frequency-weighted Hankel norm approximation with antistable weighting. These results are then applied to ℒ_∞ norm model reduction, and several numerically effective algorithms are proposed. It is shown through many numerical examples that these algorithms work very well and in many cases produce almost optimal solutions     

基于2阶Renyi熵的自适应主动噪声控制

在前馈主动噪声控制中,基于均方误差准则的传统算法仅考虑了信号的2阶统计量,忽略了实际存在的非高斯信号,不能满足对非高斯噪声的控制要求.提出基于2阶Renyi熵的滤波X自适应有限脉冲响应 (finite impulse response,FIR)主动噪声控制算法,定义2阶Renyi熵作为性能指标,利用Parzen窗方法估计误差的概率密度函数,给出基于2阶Renyi熵的信息梯度下降算法,实现自适应FIR控制,同时分析了算法的收敛性和计算复杂度.对单频信号和实测宽带非高斯噪声的仿真结果表明该算法能很好地消除非高斯噪声.     

H∞ Model Reduction for Positive Fractional Order Systems

This paper focuses on the H_∞ model reduction problem of positive fractional order systems. For a stable positive fractional order system, we aim to construct a positive reduced‐order fractional system such that the associated error system is stable with a prescribed H_∞ performance. Then, based on the bounded real lemma for fractional order systems, a sufficient condition is given to characterize the model reduction problem with a prescribed H_∞‐norm error bound in terms of a linear matrix inequality (LMI). Furthermore, by introducing a new flexible real matrix variable, the desired reduced‐order system matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable. A corresponding iterative LMI algorithm is also proposed. Finally, several illustrative examples are given to show the effectiveness of the proposed algorithms.     

Robust adaptive fault‐tolerant tracking control for uncertain linear systems with time‐varying performance bounds

In this paper, the problem of robust adaptive fault‐tolerant tracking control with time‐varying performance bounds is investigated for a class of linear systems subject to parameter uncertainties, external disturbances and actuator failures. In order to ensure the norm of the tracking error less than the user‐defined time‐varying performance bounds, we propose a new control strategy which is predicated on the generalized restricted potential function. Compared with the existing result, a novel method which provides two design freedoms is developed to reduce the tracking error. According to the online estimation information provided by adaptive mechanism, a fault‐tolerant tracking control method guaranteeing time‐varying performance bounds is developed for robust tracking of reference model. It is shown that the closed‐loop signals are bounded and the tracking error within an a priori given, time‐varying performance bounds. A simulation result is provided to demonstrate the efficacy of the proposed fault‐tolerant tracking control method.     

联合结构张量和变指数正则变分医学图像复原

利用图像局部特征,提出了一种基于[Lp]范数的变指数正则变分模型。采用结构张量作为[Lp]范数算子的自适应调整参数,克服了传统算子对噪声敏感的缺陷。从扩散的角度看,该模型是各向异性的,在图像同质区趋于平滑滤波,在图像渐变区趋于沿边缘方向扩散。该方法在扩散的同时更好地保持图像的边缘细节。实验结果表明,该方法对医学图像的复原效果优于其他几种变指数变分模型,各种客观性能指标也更佳。     

标签传播时间序列聚类的股指期货套期保值策略研究

利用时间序列聚类方法进行股指期货的套期保值,关键要选择合适的聚类方法。本文从新的视角来研究并提高时间序列聚类方法在金融数据分析领域的应用性能,提出一种基于标签传播时间序列聚类的股指期货套期保值模型。该模型以动态时间弯曲为相似性度量方法来构建现货股票网络空间结构,将每只股票看作一个节点,利用标签传播方法将节点划分到不同的簇中,最终实现股票数据聚类。另外,构建最小追踪误差优化模型来确定每支股票在现货组合中的最优权重,从而得到最优组合。实验分别比较新方法和传统聚类方法确定现货组合的追踪误差,结果表明新方法能够提高现货组合的追踪精度,为丰富金融市场投资和管理方式提供新的研究思路。