A clustering technique for the identification of piecewise affine systems

We propose a new technique for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.     

Lagrange stability and performance analysis of discrete-time piecewise affine systems with logic states

In this paper we consider discrete-time piecewise affine systems with boolean inputs, outputs and states and show that they can be represented in a logic canonical form where the logic variables influence the switching between different submodels but not the continuous-valued dynamics. We exploit this representation for studying Lagrange stability and developing performance analysis procedures based on linear matrix inequalities. Moreover, by using arguments from dissipativity theory for non-linear systems, we generalize our approach to solve the H _∞ analysis problem.     

Parameter identification of PWARX models using fuzzy distance weighted least squares method

PieceWise AutoRegressive eXogenous (PWARX) models represent one of the broad classes of the hybrid dynamical systems (HDS). Among many classes of HDS, PWARX model used as an attractive modeling structure due to its equivalence to other classes. This paper presents a novel fuzzy distance weight matrix based parameter identification method for PWARX model. In the first phase of the proposed method estimation for the number of affine submodels present in the HDS is proposed using fuzzy clustering validation based algorithm. For the given set of input–output data points generated by predefined PWARX model fuzzy c-means (FCM) clustering procedure is used to classify the data set according to its affine submodels. The fuzzy distance weight matrix based weighted least squares (WLS) algorithm is proposed to identify the parameters for each PWARX submodel, which minimizes the effect of noise and classification error. In the final phase, fuzzy validity function based model selection method is applied to validate the identified PWARX model. The effectiveness of the proposed method is demonstrated using three benchmark examples. Simulation experiments show validation of the proposed method.     

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.     

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.     

A general model for the heavy metal pollution of aquatic ecosystems: Model development

It is demonstrated how it is possible to set up a heavy metal model for an aquatic ecosystem in general. It does not imply that the same model can be applied for every case study. It is - as always - necessary to make modifications from case to case. However, by use of 5 submodels the variations from case to case are minor in the submodels, while the major question becomes which submodels to select from case to case. The 5 submodels are: a distribution model, a model of metal speciation, a model for release of metal from sediment, a model related to the metal concentrations in biota and an effect model. It is discussed which components should comprise each submodel and which modifications it should be expected to make in different cases.     

An algorithmic framework for solving large-scale multistage stochastic mixed 0-1 problems with nonsymmetric scenario trees

In this paper we present a parallelizable Branch-and-Fix Coordination algorithm for solving medium and large-scale multistage mixed 0-1 optimization problems under uncertainty. The uncertainty is represented via a nonsymmetric scenario tree. An information structuring for scenario cluster partitioning of nonsymmetric scenario trees is also presented, given the general model formulation of a multistage stochastic mixed 0-1 problem. The basic idea consists of explicitly rewriting the nonanticipativity constraints (NAC) of the 0-1 and continuous variables in the stages with common information. As a result an assignment of the constraint matrix blocks into independent scenario cluster submodels is performed by a so-called cluster splitting-compact representation. This partitioning allows to generate a new information structure to express the NAC which link the related clusters, such that the explicit NAC linking the submodels together is performed by a splitting variable representation. The new algorithm has been implemented in a C++ experimental code. Some computational experience is reported on a test of randomly generated instances as well as a large-scale real-life problem by using CPLEX as a solver of the auxiliary submodels within the open source engine COIN-OR.     

An adaptive neuro-fuzzy tracking control for multi-input nonlinear dynamic systems

An adaptive neuro-fuzzy control design is suggested in this paper, for tracking of nonlinear affine in the control dynamic systems with unknown nonlinearities. The plant is described by a Takagi–Sugeno (T–S) fuzzy model, where the local submodels are realized through nonlinear dynamical input–output mappings. Our approach relies upon the effective approximation of certain terms that involve the derivative of the Lyapunov function and the unknown system nonlinearities. The above task is achieved locally, using linear in the weights neural networks. A novel resetting scheme is proposed that assures validity of the control input. Stability analysis provides the control law and the adaptation rules for the network weights, assuring uniform ultimate boundedness of the tracking and the signals appearing in the closed-loop configuration. Illustrative simulations highlight the approach.     

On submodels and submetamodels with their relation

Model-driven engineering (MDE) recognized software models as first-class objects with their own relationships and operations, up to constitute full structured model spaces. We focus on inclusion capacities through the concepts of submodel and submetamodel which contribute a lot to the structuring effort. Submodels and submetamodels underlie many MDE practices which require their precise characterization for plain control. A typical application is model management as offered by model repositories. On the basis of results on submodel inclusion we stated in a preceding paper, we concentrate on the special form of submodels which are submetamodels and their specific role in model space structuring. Pointing out that relating submodels and submetamodels is two ways, their respective inclusion hierarchies will be systematically characterized and symmetrically compared under the logical relationships of metamodel membership and model well-formedness. As a major result, it will be shown that submodel well-formedness w.r.t submetamodels closely relates to submodel invariance (a property which guarantees transitive structure preservation) applied at both levels. The uniform formalization offers algebraic grounding to better comprehension and control of model spaces which underlie MDE activities. At a much more practical level, reusable technology which takes advantage of established results will be offered.     

Hopfield neural networks for affine invariant matching

The affine transformation, which consists of rotation, translation, scaling, and shearing transformations, can be considered as an approximation to the perspective transformation. Therefore, it is very important to find an effective means for establishing point correspondences under affine transformation in many applications. In this paper, we consider the point correspondence problem as a subgraph matching problem and develop an energy formulation for affine invariant matching by a Hopfield type neural network. The fourth-order network is investigated first, then order reduction is done by incorporating the neighborhood information in the data. Thus we can use the second-order Hopfield network to perform subgraph isomorphism invariant to affine transformation, which can be applied to an affine invariant shape recognition problem. Experimental results show the effectiveness and efficiency of the proposed method.     

Web服务器日志文件广义集成分析模型

文章以大系统理论为基础,将定性与定量分析相集合,提出了一种新型Web日志文件知识发现模型——Web服务器日志文件广义集成分析模型。同时,对模型的三种子模型:结构模型、数学模型、知识模型,分别进行了详细的分析和讨论。在此基础上,给出了优化网站结构的综合分析方法。并且以某高校网站的真实数据进行试验,结果表明该方法的实用性和有效性。     

Depth recovery and affine reconstruction under camera pure translation

This paper addresses the problems of depth recovery and affine reconstruction from two perspective images, which are generated by an uncalibrated translating camera. Firstly, we develop a new constraint that the homography for the plane, which is orthogonal to the optical axis, is determined only by the epipole and the plane's relative distance to the origin under camera pure translation. The algorithm of depth recovery is based on this new constraint, and it can successfully avoid the step of camera calibration. With the recovered depth, we show that affine reconstruction can be obtained readily. The proposed affine reconstruction does not need any control points, which were used to expand the affine coordinate system in existing method. Therefore, it could avoid the step of non-planarity verification as well as the errors from the control points. Error analysis is also presented to evaluate the uncertainty for the recovered depth value. Finally, we have tested the proposed algorithm with both simulated data and real image data. And the results show that the proposed algorithm is accurate and practical.     

A Correntropy-based Affine Iterative Closest Point Algorithm for Robust Point Set Registration

The iterative closest point (ICP) algorithm has the advantages of high accuracy and fast speed for point set registration, but it performs poorly when the point set has a large number of noisy outliers. To solve this problem, we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers. Firstly, we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model, which can avoid the influence of outliers. To maximize the objective function, we then propose a robust affine ICP algorithm. At each iteration of this new algorithm, we set up the index mapping of two point sets according to the known transformation, and then compute the closed-form solution of the new transformation according to the known index mapping. Similar to the traditional ICP algorithm, our algorithm converges to a local maximum monotonously for any given initial value. Finally, the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.      

Stratification approach for 3-D euclidean reconstruction of nonrigid objects from uncalibrated image sequences.

This paper addresses the problem of 3-D reconstruction of nonrigid objects from uncalibrated image sequences. Under the assumption of affine camera and that the nonrigid object is composed of a rigid part and a deformation part, we propose a stratification approach to recover the structure of nonrigid objects by first reconstructing the structure in affine space and then upgrading it to the Euclidean space. The novelty and main features of the method lies in several aspects. First, we propose a deformation weight constraint to the problem and prove the invariability between the recovered structure and shape bases under this constraint. The constraint was not observed by previous studies. Second, we propose a constrained power factorization algorithm to recover the deformation structure in affine space. The algorithm overcomes some limitations of a previous singular-value-decomposition-based method. It can even work with missing data in the tracking matrix. Third, we propose to separate the rigid features from the deformation ones in 3-D affine space, which makes the detection more accurate and robust. The stratification matrix is estimated from the rigid features, which may relax the influence of large tracking errors in the deformation part. Extensive experiments on synthetic data and real sequences validate the proposed method and show improvements over existing solutions.     

A feedback technique for unsatisfiable UML/OCL class diagrams

In Model‐Driven Development (MDD), detection of model defects is necessary for correct model transformations. Formal verification tools and techniques can to some extent verify models. However, scalability is a serious issue in relation to verification of complex UML/OCL class diagrams. We have proposed a model slicing technique that slices the original model into submodels to address the scalability issue. A submodel can be detected as unsatisfiable if there are no valid values for one or more attributes of an object in the diagram or if the submodel provides inconsistent conditions on the number of objects of a given type. In this paper, we propose a novel feedback technique through model slicing that detects unsatisfiable submodels and their integrity constraints among the complex hierarchy of an entire UML/OCL class diagram. The software developers can therefore focus their revision efforts on the incorrect submodels while ignoring the rest of the model. Copyright © 2013 John Wiley & Sons, Ltd.     

Remote sensing image matching by integrating affine invariant feature extraction and RANSAC

A new technical framework for remote sensing image matching by integrating affine invariant feature extraction and RANSAC is presented. The novelty of this framework is an automatic optimization strategy for affine invariant feature matching based on RANSAC. An automatic way to determine the distance threshold of RANSAC is proposed, which is a key problem to implement this RANSAC-based automatic optimization. Since affine invariant feature matching technology has been successfully applied to remote sensing image matching, we design an experiment to compare the proposed framework (with optimization) with the standard affine invariant feature matching (without optimization). By using three pairs with different types of imagery, the experimental results indicate that the proposed framework can always get higher correctness of image matching in automatic way, compared to the standard affine invariant feature matching technology.     

Affine Curvature Scale Space with Affine Length Parametrisation

The maxima of Curvature Scale Space (CSS) image have been used to represent 2D shapes under affine transforms. The CSS image is expected to be in the MPEG-7 package of standards. Since the CSS image employs the arc length parametrisation which is not affine invariant, we expect some deviations in the maxima of the CSS image under general affine transforms. Affine length and affine curvature have already been introduced and used as alternatives to arc length and conventional curvature in affine transformed environments. The utility of using these parameters to enrich the CSS representation is addressed in this paper. We use arc length to parametrise the curve prior to computing its CSS image. The parametrisation has been proven to be invariant under affine transformation and has been used in many affine invariant shape recognition methods. Since the organisation of the CSS image is based on curvature zero crossings of the curve, in this paper, we also investigate the advantages and shortcomings of using affine curvature in computation of the CSS image. The enriched CSS representations are then used to find similar shapes from a very large prototype database, and also a small classified database, both consisting of original as well as affine transformed shapes. An improvement is observed over the conventional CSS image.     

Reach control problem for affine multi-agent dynamic systems on simplices by affine feedback

Aiming at the reach control problem for a multi-agent system composed of affine coupling systems, an affine controller is proposed. Different from affine single-agent systems, additional difficulties are faced for multi-agent systems on the reach control because of the coupling between agents. In this paper, we use the compactness and convexity of the simplex to overcome the above difficulties, and propose a sufficient condition to solve the reach control problem for multi-agent systems, which aims to detect an affine feedback control such that each agent in the system first leaves a given simplex through a prespecified facet rather than a certain restricted facet in a finite time. In addition, necessary conditions for the solvability of the problem are obtained. Finally, the validity of the results is verified by a three-dimensional numerical example.     

Classification and stabilizability analysis of bimodal piecewise affine systems

This paper presents a classification of bimodal piecewise affine systems from the viewpoint of well‐posedness. First, we address the feedback well‐posedness problem of a general class of bimodal piecewise affine systems, which is the problem of feedback equivalence to a well‐posed system. Next, based on this result, we classify all feedback well‐posed systems into four classes to address the control problem of piecewise affine systems in a systematic way. As its application, the stabilizability problem with well‐posedness is discussed for each class, and several remarks on stabilizability are given. Copyright © 2002 John Wiley & Sons, Ltd.