Nonlinear model predictive control for path following problems

This paper presents a general nonlinear model predictive control scheme for path following problems. Path following problem of nonlinear systems is transformed into a parameter‐dependent regulation problem. Sufficient conditions for recursive feasibility and asymptotic convergence of the given scheme are presented. Furthermore, a polytopic linear differential inclusion‐based method of choosing a suitable terminal penalty and the corresponding terminal constraint are proposed. To illustrate the implementation of the nonlinear model predictive control scheme, the path following problem of a car‐like mobile robot is discussed, and the control performance is confirmed by simulation results. Copyright © 2014 John Wiley & Sons, Ltd.     

A regularization framework for robust dimensionality reduction with applications to image reconstruction and feature extraction

Dimensionality reduction has many applications in pattern recognition, machine learning and computer vision. In this paper, we develop a general regularization framework for dimensionality reduction by allowing the use of different functions in the cost function. This is especially important as we can achieve robustness in the presence of outliers. It is shown that optimizing the regularized cost function is equivalent to solving a nonlinear eigenvalue problem under certain conditions, which can be handled by the self-consistent field (SCF) iteration. Moreover, this regularization framework is applicable in unsupervised or supervised learning by defining the regularization term which provides some types of prior knowledge of projected samples or projected vectors. It is also noted that some linear projection methods can be obtained from this framework by choosing different functions and imposing different constraints. Finally, we show some applications of our framework by various data sets including handwritten characters, face images, UCI data, and gene expression data.     

一种小波变换模极大值的扩散模型

遥感图像的噪声分析、评估和滤波一直是遥感图像处理的一个重要研究领域。近年来,基于非线性扩散模型的图像去噪方法因其在对图像进行去噪的同时,对图像的特征信息具有一定的保护作用而受到遥感图像应用领域的关注并成为研究热点。针对P-M方程和ALM模型在去除遥感高斯噪声时所存在的对图像强边缘附近的噪声难以去除和可能造成奇异点的模糊或丢失等问题,将小波变换模极大值进入到扩散模型中提出一种新的非线性扩散模型,并给出模型的离散化算法。该模型有效地克服了P-M模型和ALM模型在图像去噪过程中的不足,在有效去除噪声的同时,很好地保留了遥感图像的边缘和纹理细节信息。实验结果验证了所提出模型的有效性和稳定性。     

基于伪测量法的直链式N体空间绳系系统约束状态估计

针对直链式N体空间绳系系统（STS）,将系绳绳长作为先验信息,在仅使用2个GPS（全球定位系统）传感器的条件下,提出了一种基于伪测量法的约束状态估计方法。首先,基于Udwadia-Kalaba方法建立了一种新颖的直链式N体STS通用动力学模型。然后,针对GPS传感器更新频率低和非线性系统模型线性化过程中雅可比矩阵计算复杂的问题,开发了一种改进的平方根无迹卡尔曼滤波（IUKF）算法。同时,基于李导数的局部弱可观的秩判据方法严格证明了本文估计方法的可观性。最后,仿真验证了本文方法的有效性。仿真结果表明所提方法能够保证系统状态估计精度和跟踪实时性。     

基于边缘信赖度和形状相似性的超声图像分割方案

为了对低信噪比的超声图像进行有效分割,提出了一种新的超声图像分割方案,该方案由各向异性扩散方程和蛇模型组成。首先通过对蛇模型算法进行改进,并利用预先知道的形状信息,提出了一种基于形状相似性的参数自调整蛇模型;同时还对各向异性扩散方程进行了修正,提出了基于边缘信赖度的改进算法,以提高各向异性扩散方程的去噪能力。实验结果表明,该方法不但缓解了由于超声图像信噪比过低而影响分割的问题,同时实现了蛇模型的参数自适应设置,可见是一种有效的图像分割算法。     

Observer‐based adaptive neural control for a class of nonlinear singular systems

The problem of observer‐based adaptive neural control via output feedback for a class of uncertain nonlinear singular systems is studied in this article. The nonlinear singular systems can be regarded as two subsystems that are coupled with each other: differential subsystem and algebraic subsystem. The differential systems can be nonstrict feedback structures. To guarantee that the singular system is regular and impulse‐free, two new conditions are proposed. By the conditions, the linear controller and observer, which are used to estimate the immeasurable state variables, are obtained. Then, an output feedback scheme through adaptive neural backstepping is proposed to ensure that all states of the closed‐loop system are semiglobally uniformly ultimately bounded and converge to a small neighborhood of the origin. Simulation examples illustrate the effectiveness of the presented method.     

Lipschitz广义非线性系统观测器设计

研究一类广义非线性系统的观测器设计问题．首先讨论了半正定Lyapunov函数下指数1广义非线性系统稳定及渐近稳定性,然后对一类由线性和Lipschitz非线性项组成的广义非线性系统,给出了渐近稳定观测器存在的条件,并把观测器反馈增益矩阵的设计归结为广义线性系统容许控制以及奇异值计算问题,证明了若容许广义线性系统矩阵的最小奇异值大于系统的Lipschitz常数,容许控制器增益矩阵就是待求的观测器反馈增益矩阵。     

On computation of the stability radius for nonlinearly structured perturbations

This paper considers the problem of finding a perturbation matrix with the least spectral norm such that a matrix-valued function becomes singular, where the dependence of the function on the perturbation is allowed to be nonlinear. It is proved that such a problem can be approximated by a smooth unconstrained minimization problem with compact sublevel sets. A computational procedure proposed based on this result is demonstrated to be effective in both linear and nonlinear cases.     

A post nonlinear geometric algorithm for independent component analysis

Simple linear independent component analysis (ICA) algorithms work efficiently only in linear mixing environments. Whereas, a nonlinear ICA model, which is more complicated, would be more practical for general applications as it can work with both linear and nonlinear mixtures. In this paper, we introduce a novel method for nonlinear ICA problem. The proposed method follows the post nonlinear approach to model the mixtures, and exploits the difference between a linear mixture and a nonlinear one from their nature of distributions in a multidimensional space to develop a separation scheme. The nonlinear mixture is represented by a nonlinear surface while the linear mixture is represented by a plane. A geometric learning algorithm named as post nonlinear geometric ICA (pnGICA) is developed by geometrically transforming the nonlinear surface to a plane, i.e., to a linear mixture. Computer simulations of the algorithm provide promising performance on different data sets.     

On computation of the stability radius for nonlinearly structured perturbations

This paper considers the problem of finding a perturbation matrix with the least spectral norm such that a matrix-valued function becomes singular, where the dependence of the function on the perturbation is allowed to be nonlinear. It is proved that such a problem can be approximated by a smooth unconstrained minimization problem with compact sublevel sets. A computational procedure proposed based on this result is demonstrated to be effective in both linear and nonlinear cases.     

基于核的多元区别分析算法的特征抽取及其在人脸识别中的应用

提出了一种基于核技术的求多元区别分析最佳解的K1PMDA算法，并把这一算法应用于人脸识别中。对线性人脸识别中存在两个突出问题：1、在光照、表情、姿态变化较大时，人脸图像分类是复杂的、非线性的；2、小样本问题，即当训练样本数量小于样本特征空间维数时，导致类内散布矩阵奇异。对于前一个问题，可以采用核技术提取人脸图像样本的非线性特征，对于后一个问题，采用加入一个扰动参数的扰动算法。通过对ORL，Yale Group B以及UMIST三个人脸库的实验表明，该算法是可行的、高效的。     

Finite frequency fault detection for T-S fuzzy singular multiple timedelay systems

This paper focuses on the problem of fault detection (FD) for a class of nonlinear systems described by the T-S fuzzy singular model with multiple time delays and actuator faults. Two finite-frequency performance indices are introduced to measure fault sensitivity and disturbance robustness. To reduce the conservatism of the existing results, a finite frequency domain approach to fuzzy singular multiple time-delay systems is proposed. Then based on the approach, filter design conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). Finally, simulation studies are provided to demonstrate the application of the proposed method.     

Image quality assessment method based on nonlinear feature extraction in kernel space

To match human perception, extracting perceptual features effectively plays an important role in image quality assessment. In contrast to most existing methods that use linear transformations or models to represent images, we employ a complex mathematical expression of high dimensionality to reveal the statistical characteristics of the images. Furthermore, by introducing kernel methods to transform the linear problem into a nonlinear one, a full-reference image quality assessment method is proposed based on high-dimensional nonlinear feature extraction. Experiments on the LIVE, TID2008, and CSIQ databases demonstrate that nonlinear features offer competitive performance for image inherent quality representation and the proposed method achieves a promising performance that is consistent with human subjective evaluation.     

A Linear Image Reconstruction Framework Based on Sobolev Type Inner Products

Exploration of information content of features that are present in images has led to the development of several reconstruction algorithms. These algorithms aim for a reconstruction from the features that is visually close to the image from which the features are extracted. Degrees of freedom that are not fixed by the constraints are disambiguated with the help of a so-called prior (i.e. a user defined model). We propose a linear reconstruction framework that generalizes a previously proposed scheme. The algorithm greatly reduces the complexity of the reconstruction process compared to non-linear methods. As an example we propose a specific prior and apply it to the reconstruction from singular points. The reconstruction is visually more attractive and has a smaller 핃₂-error than the reconstructions obtained by previously proposed linear methods. Bart Jansen, Frans Kanters and Remco Duits are joint main authors of this article.     

DELAY‐DEPENDENT ROBUST CONTROL OF DESCRIPTOR SYSTEMS WITH TIME DELAY

This paper deals with the problem of stability and robust control for both certain and uncertain continuous‐time singular systems with state delay. Systems with norm‐bounded parameter uncertainties are considered. Robust delay‐dependent stability criteria and linear memoryless state feedback controllers based on linear matrix inequality are obtained. By choosing some Lyapunov‐Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay‐dependent results. Finally, numerical example is provided to illustrate the effectiveness of the proposed method.     

非线性广义系统的变结构控制设计

从线性定常广义系统出发，研究非线性广义系统的变结构控制设计问题。其主要思想为：选取一具有指定性能的线性定常广义系统作为参考模型，根据所控系统与参考模型的误差方程设计变结构控制，使系统的状态（输出）向参考模型的状态（输出）逼近，由参考模型的性能即得所研究的非线性广义系统所希望的性能。仿真例子验证了所建立方法的有效性。     

Robust fault diagnosis scheme in a class of nonlinear system based on UIO and fuzzy residual

In this study, a novel robust fault diagnosis scheme is developed for a class of nonlinear systems when both fault and disturbance are considered. The proposed scheme includes both component and sensor fault with nonlinear system that transferred to nonlinear Takagi-Sugeno (T-S) model. It considers a larger category of nonlinear system when fuzzification is used for only nonlinear distribution matrices. In fact the proposed method covers nonlinear systems could not transform to linear T-S model. This paper studies the problem of robust fault diagnosis based on two fuzzy nonlinear observers, the first one is a fuzzy nonlinear unknown input observer (FNUIO) and the other is a fuzzy nonlinear Luenberger observer (FNLO). This approach decouples the faulty subsystem from the rest of the system through a series of transformations. Then, the objective is to design FNUIO to guarantee the asymptotic stability of the error dynamic using the Lyapunov method; meanwhile, FNLO is designed for faulty subsystem to generate fuzzy residual signal based on a quadratic Lyapunov function and some matrices inequality convexification techniques. FNUIO affects only the fault free subsystem and completely removes any unknown inputs such as disturbances when residual signal is generated by FNLO is affected by component or sensor fault. This novelty and using nonlinear system in T-S model make the proposed method extremely effective from last decade literature. Sufficient conditions are established in order to guarantee the convergence of the state estimation error. Thus, a residual generator is determined on the basis of LMI conditions such that the estimation error is completely sensitive to fault vector and insensitive to the unknown inputs. Finally, an numerical example is given to show the highly effectiveness of the proposed fault diagnosis scheme.     

Kernel machine-based one-parameter regularized fisher discriminant method for face recognition.

This paper addresses two problems in linear discriminant analysis (LDA) of face recognition. The first one is the problem of recognition of human faces under pose and illumination variations. It is well known that the distribution of face images with different pose, illumination, and face expression is complex and nonlinear. The traditional linear methods, such as LDA, will not give a satisfactory performance. The second problem is the small sample size (S3) problem. This problem occurs when the number of training samples is smaller than the dimensionality of feature vector. In turn, the within-class scatter matrix will become singular. To overcome these limitations, this paper proposes a new kernel machine-based one-parameter regularized Fisher discriminant (K1PRFD) technique. K1PRFD is developed based on our previously developed one-parameter regularized discriminant analysis method and the well-known kernel approach. Therefore, K1PRFD consists of two parameters, namely the regularization parameter and kernel parameter. This paper further proposes a new method to determine the optimal kernel parameter in RBF kernel and regularized parameter in within-class scatter matrix simultaneously based on the conjugate gradient method. Three databases, namely FERET, Yale Group B, and CMU PIE, are selected for evaluation. The results are encouraging. Comparing with the existing LDA-based methods, the proposed method gives superior results.     

Regulation of linear continuous-time singular systems with constrained states and controls

This article considers the constrained regulation problem (CRP) for linear continuous-time singular systems. The study consists in finding for a completely controllable singular system a linear state feedback control law that eliminates the impulsive behavior of a system and transfers asymptotically to the origin all initial states belonging to some polyhedral subset of the state space while respecting the linear constraints on state and control vectors. The proposed method gives a solution to the CRP for a singular system from a transformation that leads to a problem of positive invariance for a reduced order nonsingular one. Conditions guaranteeing the positive invariance for the whole domain of admissible controls are deduced. It is shown that the solution to the CRP is that of a nonlinear algebraic matrix equation.     

A hybrid linear/nonlinear training algorithm for feedforward neuralnetworks

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.