Clustering based multiple model control of hybrid dynamical systems using HJB solution

This paper deals with Hamilton–Jacobi–Bellman (HJB) equation based stabilized optimal control of hybrid dynamical systems (HDS). This paper presents the fuzzy clustering based event wise multiple linearized modeling approaches for HDS to describe the continuous dynamic in each event. In the present work a fuzzy clustering validation approach is presented for the selection of number of linearized models which span entire HDS. The method also describes how to obtain event wise operating point using fuzzy membership function, which is used to find the event wise model bank by linearizing the first principles model. The event wise linearized models are used for the formulation of the optimal control law. The HJB equation is formulated using a suitable quadratic term in the objective function. By use of the direct method of Lyapunov stability, the control law is shown to be optimal with respect to objective functional and stabilized the event wise linearized models. The global Lyapunov function is proposed with discrete variables which stabilized the HDS. The proposed modeling and control algorithm have been applied on two HDSs. Necessary theoretical and simulation experiments are presented to demonstrate the performance and validation of the proposed algorithm.     

Identification of piecewise affine systems based on statistical clustering technique

This paper is concerned with the identification of a class of piecewise affine systems called a piecewise affine autoregressive exogenous (PWARX) model. The PWARX model is composed of ARX sub-models each of which corresponds to a polyhedral region of the regression space. Under the temporary assumption that the number of sub-models is known a priori, the input-output data are collected into several clusters by using a statistical clustering algorithm. We utilize support vector classifiers to estimate the boundary hyperplane between two adjacent regions in the regression space. In each cluster, the parameter vector of the sub-model is obtained by the least squares method. It turns out that the present statistical clustering approach enables us to estimate the number of sub-models based on the information criteria such as CAIC and MDL. The estimate of the number of sub-models is performed by applying the identification procedure several times to the same data set, after having fixed the number of sub-models to different values. Finally, we verify the applicability of the present identification method through a numerical example of a Hammerstein model.     

Weighted least squares based recursive parametric identification for the submodels of a PWARX system

A piecewise affine autoregressive system with exogenous inputs (PWARX) is composed of a finite number of ARX subsystems, each of which corresponds to a polyhedral partition of the regression space. In this work a weighted least squares (WLS) estimator is suggested to recursively estimate the parameters of the ARX submodels, in which a sequence of kernel functions are introduced. Conditions on the input signal and the PWARX system are imposed to guarantee the almost sure convergence of the WLS estimates. Some numerical examples are included to illustrate performances of the algorithm.     

Modeling and advanced control method of PVC polymerization process

Based on data driven modeling theory, PVC polymerization process modeling and intelligent optimization control algorithm is studied. Firstly, a multi-T–S fuzzy neural networks soft-sensing model combining the principal component analysis (PCA) and fuzzy c-means (FCM) clustering algorithm is proposed to predict the convention rate and velocity of Vinyle Chloride Monomer (VCM). The proposed hybrid learning algorithm utilizing the harmony search (HS) and least square method is used to adjust the model premise parameters and consequent parameters. Secondly, the generalized predictive control (GPC) algorithm of polymerizer temperature based on segmental affine is proposed. According to dynamic equation of polymerizer temperature deduced by heat balance mechanism, the segmental affine model is built by temperature and convention rate of the polymerizer. Then linear matrix inequality (LMI) method is used to design the controller. Finally, simulation results and industrial application show the validity and feasibility of the proposed control strategy.     

A bounded-error approach to piecewise affine system identification

This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.     

基于w-距离均值的模糊聚类算法

针对模糊C-均值(FCM)算法易陷入局部最优值以及对聚类中心和噪声数据敏感问题,提出了一种基于w-距离均值的模糊聚类算法。首先根据数据自身的分布规律,依据样本间距离均值思想确定初始聚类中心,并引入了调衡因子w来调节距离均值阈值;其次为每个样本赋予权值,并利用样本权值修改了聚类中心公式和目标函数公式,提高了算法的抗噪性;最后实验结果验证了所提算法可以有效地解决聚类效果往往受初始聚类中心的影响的问题,避免了局部收敛,增强了抗噪性,准确率和效率较高。     

公理化模糊共享近邻自适应谱聚类算法

针对传统的谱聚类算法通常利用高斯核函数作为相似性度量,且单纯以距离决定相似性不能充分表现原始数据中固有的模糊性、不确定性和复杂性,导致聚类性能降低的问题。提出了一种公理化模糊共享近邻自适应谱聚类算法,首先结合公理化模糊集理论提出了一种模糊相似性度量方法,利用识别特征来衡量更合适的数据成对相似性,然后采用共享近邻的方法发现密集区域样本点分布的结构和密度信息,并且根据每个点所处领域的稠密程度自动调节参数σ,从而生成更强大的亲和矩阵,进一步提高聚类准确率。实验表明,相较于距离谱聚类、自适应谱聚类、模糊聚类方法和地标点谱聚类,所提算法有着更好的聚类性能。     

Dual-centers type-2 fuzzy clustering framework and its verification and validation indices

In this paper we present a clustering framework for type-2 fuzzy clustering which covers all steps of the clustering process including: clustering algorithm, parameters estimation, and validation and verification indices. The proposed clustering algorithm is developed based on dual-centers type-2 fuzzy clustering model. In this model the centers of clusters are defined by a pair of objects rather than a single object. The membership values of the objects to the clusters are defined by type-2 fuzzy numbers and there are not any type reduction or defuzzification steps in the proposed clustering algorithm. In addition, the relation among the size of the cluster bandwidth, distance between dual-centers and fuzzifier parameter are indicated and analyzed to facilitate the parameters estimation step. To determine the optimum number of clusters, we develop a new validation index which is compatible with the proposed model structure. A new compatible verification index is also defined to compare the results of the proposed model with existing type-1 fuzzy clustering model. Finally, the results of computational experiments are presented to show the efficiency of the proposed approach.     

基于半监督模糊C均值算法的遥感影像分类

遥感影像数据因其固有的不确定性与复杂性,导致传统的无监督分类算法难以对其准确建模。基于模糊集理论的模式识别方法可以有效地表达数据的模糊性,其中二型模糊集能更好地刻画类间多重不确定性,而半监督法可以利用少量先验知识来解决算法对数据的泛化性问题,因此提出一种基于半监督的自适应区间二型模糊C均值遥感影像分类方法（SS-AIT2FCM）。首先,结合半监督和进化论思想,提出一种新的模糊权重指数选取方法,以提升自适应区间二型模糊C均值聚类算法的鲁棒性与泛化性,使算法更适用于光谱混叠严重、覆盖面积大、地物丰富的遥感数据分类;然后,通过对少量标记样本的软约束监督,对区间二型模糊算法迭代过程进行优化指导,来挖掘数据的最优表达。实验选用了北京颐和园区域的SPOT5多光谱遥感影像数据和广东横琴岛区域的Landsat TM多光谱遥感影像数据,对现有流行的模糊分类算法和SS-AIT2FCM的分类结果进行了比较。结果表明,SS-AIT2FCM获得了更高的分类精度与更清晰的类别边界,且有较好数据泛化能力。     

一种基于密度峰值的针对模糊混合数据的聚类算法

将CFSFDP算法拓展到连续型模糊集和离散型模糊集上,提出了一种针对模糊混合数据的拓展型CFSFDP算法,将其命名为FMD-CFSFDP算法。FMD-CFSFDP算法将样本涵盖的经典信息拓展到了模糊集上,利用寻找密度峰值的方法对模糊样本进行聚类,这是一种建立在模糊集上针对模糊混合数据的基于密度的聚类算法。首先简单介绍了CFSFDP算法及其改进,给出了"模糊混合数据"的数学概念;然后结合传统模糊欧氏距离的概念,分别提出了误差更小的针对连续型模糊集与离散型模糊集的改进型欧氏距离,在此基础上,依托权值构建了针对混合型模糊数据的整体距离。参考CFSFDP算法的聚类步骤给出了FMD-CFSFDP算法的聚类步骤。随后,在不同样本量、不同指标数量、不同簇数、不同取数规则的条件下,对算法进行了随机模拟实验并对聚类结果进行了分析。最后分别总结了FMD-CFSFDP算法的优缺点,并在此基础上提出了改进方案,为今后深入研究提供了参考。     

基于模糊等价矩阵的无线传感器聚类分区算法

基于模糊等价矩阵的聚类方法是模糊聚类中一种经典的分析方法。首次将其引入无线传感器节点分区的应 用中。该聚类分区算法通过计算节点间的Euclid距离、分析其相关性、形成模糊等价矩阵、进行节点分区,实现了对 该分区算法的应用设计。分析了其算法时间复杂度,并利用Matlab软件完成了算法仿真。仿真结果显示,该算法可 以根据其疏密程度的不同很好地将无线传感节点分成不同区域。     

神经模糊系统中模糊规则的优选

提出一种基于两级聚类算法的自组织神经模糊系统，该系统采用两级聚类算法（改进的最近邻域聚类算法和Gustafson-Kessel模糊聚类算法）对输入／输出数据进行模糊聚类，并由模糊聚类的划分熵确定最优划分，建立模糊模型，模型精度可由梯度下降法进一步提高。仿真结果表明，这种神经模糊系统具有结构简单、规则数少、学习速度快以及建模精度高等特点。     

A clustering-based approach for the identification of a class of temporally switched linear systems

The behaviours of hybrid dynamic systems (HDS) are determined by combining continuous variables with discrete switching logic. The identification of a HDS aims to find an accurate model of the system’s dynamics based on its past inputs and outputs. In pattern recognition (PR) methods, each mode is represented by a set of similar patterns that form restricted regions in the feature space. These sets of patterns are called classes. A pattern is a vector built from past inputs and outputs. HDS identification is a challenging problem since it involves the estimation of different sets of parameters without knowing in advance which sections of the measured data correspond to the different modes of the system. Therefore, HDS identification can be achieved by combining two steps: clustering and parameter estimation. In the clustering step, the number of discrete modes (i.e., the classes that input-output data points belong) is estimated. The parameter estimation step finds the parameters of the models that govern the continuous dynamics in each mode. In this paper, an unsupervised PR method is proposed to achieve the clustering step of the identification of temporally switched linear HDS. The determination of the number of modes does not require prior information about the modes or their number.     

Fuzzy relational classifier trained by fuzzy clustering

A novel approach to nonlinear classification is presented, in the training phase of the classifier, the training data is first clustered in an unsupervised way by fuzzy c-means or a similar algorithm. The class labels are not used in this step. Then, a fuzzy relation between the clusters and the class identifiers is computed. This approach allows the number of prototypes to be independent of the number of actual classes. For the classification of unseen patterns, the membership degrees of the feature vector in the clusters are first computed by using the distance measure of the clustering algorithm. Then, the output fuzzy set is obtained by relational composition. This fuzzy set contains the membership degrees of the pattern in the given classes. A crisp decision is obtained by defuzzification, which gives either a single class or a "reject" decision, when a unique class cannot be selected based on the available information. The principle of the proposed method is demonstrated on an artificial data set and the applicability of the method is shown on the identification of live-stock from recorded sound sequences. The obtained results are compared with two other classifiers.     

一种模糊相似关系的基因表达数据聚类方法

对于时间序列的基因表达数据,传统的聚类算法都是以距离为相似性度量标准,没有考虑基因随时间变化的相似趋势。从基因变化的趋势出发,构造了一种新的模糊相似关系矩阵,提出了改进的基于模糊相似关系的聚类算法,并以该算法计算FCM的初始聚类中心。将该方法应用在酵母菌基因表达数据中,实验结果表明该算法不仅克服了FCM算法易陷入局部极小值、对初值敏感的缺点,而且能够发现一些表达模式变化趋势相似的共调控基因。     

基于清晰半径的模糊点二次聚类算法

针对模糊C-均值(FCM)聚类算法在模糊边界上容易出现划分错误的问题,提出一种对模糊点进行二次处理的改进算法。该算法以各类中的数据分布密度为依据,首先利用清晰点构成超球体中心区域,然后基于中心区域的清晰半径定义一种新的相似性距离,并利用该距离对模糊点的隶属度进行二次计算,重新确定其类别归属。实验结果显示,改进算法能有效纠正分类错误,提高模糊点的清晰度,在密度差异较大的数据集上具有一定的应用潜力。     

基于混合距离学习的鲁棒的模糊C均值聚类算法

距离度量对模糊聚类算法FCM的聚类结果有关键性的影响。实际应用中存在这样一种场景,聚类的数据集中存在着一定量的带标签的成对约束集合的辅助信息。为了充分利用这些辅助信息,首先提出了一种基于混合距离学习方法,它能利用这样的辅助信息来学习出数据集合的距离度量公式。然后,提出了一种基于混合距离学习的鲁棒的模糊C均值聚类算法（HR-FCM算法）,它是一种半监督的聚类算法。算法HR-FCM既保留了GIFP-FCM（Generalized FCM algorithm with improved fuzzy partitions）算法的鲁棒性等性能,也因为所采用更为合适的距离度量而具有更好的聚类性能。实验结果证明了所提算法的有效性。     

基于加权直觉模糊集合的聚类模型

针对已有基于直觉模糊集的聚类方法的局限性,提出了一种基于加权直觉模糊集合的聚类模型——WIFSCM。在该模型中,提出了特定特征空间下的等价样本和加权直觉模糊集合的概念;并推导出基于等价样本和加权直觉模糊集合的直觉模糊聚类算法的目标函数,利用该目标函数推导出直觉模糊聚类中心迭代算法和隶属度矩阵迭代算法;定义了基于加权直觉模糊集合的密度函数,确定了初始聚类中心,减少了迭代次数。通过灰度图像分割实验,证明了该模型的有效性,同时与普通直觉模糊集FCM聚类算法(IFCM)相比,聚类速度提高近百倍。     

基于改进的粒子群算法和信息熵的知识获取方法

针对粒子群优化算法（PSO）易陷入局部优化的问题,在PSO算法加入交叉变异算子,克服了标准PSO算法易陷入局部最优的不足;并将改进的PSO算法和模糊C 均值聚类相结合,提出了一种新的模糊聚类算法CMPSO FCM,该算法具有良好的搜索能力和聚类效果。进而将聚类得到的属性隶属矩阵用于属性约简,并提出一种基于信息熵的模糊粗糙集知识获取的方法。实验和实例分析表明该方法的正确性和有效性。     

一种基于特征属性的Web用户模糊聚类改进算法

为降低传统FCM算法的计算复杂性,提高Web用户聚类的效果,文中提出了一种改进的基于特征属性的Web用户模糊聚类算法。首先通过用户访问页面的次数和时间建立Web用户兴趣度矩阵,并根据商品的特征属性值将Web用户兴趣度矩阵映射为用户对特征属性的偏好矩阵,从而有效降低数据稀疏性;然后以此为数据集,对传统的FCM算法进行了改进,将聚类中心分为活动和稳定两种,忽略稳定聚类中的距离计算以降低计算复杂性。最后通过仿真实验证实了新算法的有效性和可行性。