具有非线性扰动的广义系统的鲁棒H∞控制

研究具有非线性结构扰动广义系统的鲁棒H∞控制和鲁棒H∞保性能控制问题,该不确定性为时间和状态的函数.且满足Lipschitz条件.目的是分别设计系统的鲁棒H∞控制器和鲁棒H∞保性能控制器.应用线性矩阵不等式方法,分别给出了系统的鲁棒H∞控制器和鲁棒H∞保性能控制器存在的充分条件.当这些条件可解时,分别给出了鲁棒H∞控制器和鲁棒H∞保性能控制器的表达式.最后通过一个仿真算例说明了所给出方法的应用.     

Guided Sampling via Weak Motion Models and Outlier Sample Generation for Epipolar Geometry Estimation

The problem of automatic robust estimation of the epipolar geometry in cases where the correspondences are contaminated with a high percentage of outliers is addressed. This situation often occurs when the images have undergone a significant deformation, either due to large rotation or wide baseline of the cameras. An accelerated algorithm for the identification of the false matches between the views is presented. The algorithm generates a set of weak motion models (WMMs). Each WMM roughly approximates the motion of correspondences from one image to the other. The algorithm represents the distribution of the median of the geometric distances of a correspondence to the WMMs as a mixture model of outlier correspondences and inlier correspondences. The algorithm generates a sample of outlier correspondences from the data. This sample is used to estimate the outlier rate and to estimate the outlier pdf. Using these two pdfs the probability that each correspondence is an inlier is estimated. These probabilities enable guided sampling. In the RANSAC process this guided sampling accelerates the search process. The resulting algorithm when tested on real images achieves a speedup of between one or two orders of magnitude. This work was supported partly by grant 01-99-08430 of the Israeli Space Agency through the Ministry of Science Culture and Sports of Israel.     

A simple linear hidden-line algorithm for star-shaped polygons

A very simple, linear-running-time algorithm is presented for solving the hidden-line problem for star-shaped polygons. The algorithm first decomposes the visibility regions into edge-visible polygons and then solves the hidden-line problem for these simpler polygons. In addition to simplicity the algorithm possesses the virtue of affording a very easy proof of correctness. Some applications where this problem arises are mentioned.     

Computing the update of the repeated median regression line in linear time

The repeated median line estimator is a highly robust method for fitting a regression line to a set of n data points in the plane. In this paper, we consider the problem of updating the estimate after a point is removed from or added to the data set. This problem occurs, e.g., in statistical online monitoring, where the computational effort is often critical. We present a deterministic algorithm for the update working in O(n) time and O(n²) space.     

Numerical solution of singular perturbation problems

A finite difference method for Second Order Singular Perturbation Problems is presented. It is based on a mesh selection strategy derived by using sufficient conditions which ensure the well conditioning of tridiagonal matrices. In particular the implementation aspects of the method are discussed. Numerical tests are reported to evidence the effectiveness of this method and its competitiveness with respect to known solvers for BVPs. Work performed within the activities of the project ‘Matematica Computazionale’ supported by MURST 40%.     

Buckling load optimization for heavy elastic columns: a perturbation approach

This paper discusses the problem of achieving the weight distribution of a column, along its height, that optimizes the buckling load of the column, taking into consideration the column self-weight. The field equations of optimality and stability were generated through variational principles and solved by applying the method of perturbation. Results obtained have shown that for the optimal buckling load of a plane-tapered column, the distribution of the cross-sectional area along the column axis follows a perturbed parabolic law. The optimal column has a buckling load which is 21.58% larger than that of the corresponding uniform column with the same volume and height.     

Uncertainty analysis of structural systems by perturbation techniques

The formulation of an efficient method to evaluate the uncertainty of the structural response by applying perturbation techniques is described. Structural random variables are defined by their mean values, standard deviations and correlations. The uncertainty of structural behaviour is evaluated by the covariance matrix of response according to the developed perturbation methodology. It is also presented the procedure used to implement this method in a structural finite element framework. The implemented computational program allows, in only one structural analysis, to evaluate the mean value and the standard deviation of the structural response, defined in terms of displacements or forces. The proposed method is exact for problems with linear design functions and normal-distributed random variables. Results remain accurate for non-linear design functions if they can be approximated by a linear combination of the basic random variables.     

Trends and Developments in Computational Geometry

This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry and computer graphics closer together.     

MPC for stable linear systems with model uncertainty

In this paper, we developed a model predictive controller, which is robust to model uncertainty. Systems with stable dynamics are treated. The paper is mainly focused on the output-tracking problem of a system with unknown steady state. The controller is based on a state-space model in which the output is represented as a continuous function of time. Taking advantage of this particular model form, the cost functions is defined in terms of the integral of the output error along an infinite prediction horizon. The model states are assumed perfectly known at each sampling instant (state feedback). The controller is robust for two classes of model uncertainty: the multi-model plant and polytopic input matrix. Simulations examples demonstrate that the approach can be useful for practical application.     

A new kernel-based approach for linear system identification

This paper describes a new kernel-based approach for linear system identification of stable systems. We model the impulse response as the realization of a Gaussian process whose statistics, differently from previously adopted priors, include information not only on smoothness but also on BIBO-stability. The associated autocovariance defines what we call a stable spline kernel. The corresponding minimum variance estimate belongs to a reproducing kernel Hilbert space which is spectrally characterized. Compared to parametric identification techniques, the impulse response of the system is searched for within an infinite-dimensional space, dense in the space of continuous functions. Overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization. The proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two-step procedure that projects the nonparametric estimate onto the space of nominal models. The continuous-time derivation immediately extends to the discrete-time case. On several continuous- and discrete-time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques.     

Perturbation analysis of fuzzy linear systems

This paper deals with the perturbation analysis of fuzzy linear systems. Three cases of perturbation are considered: (a) the right hand side is perturbed while the coefficient matrix remains unchanged; (b) the coefficient matrix is perturbed while the right hand side remains unchanged, and (c) both the coefficient matrix and the right hand side are perturbed. For all of the three cases, the respective relative error bounds for solutions of fuzzy linear system are derived. The results are illustrated by numerical examples.     

Series expansions for analytic systems linear in control

This paper presents a series expansion for the evolution of a class of nonlinear systems characterized by constant input vector fields. We present a series expansion that can be computed via explicit recursive expressions, and we derive sufficient conditions for uniform convergence over the finite- and infinite-time horizon. Furthermore, we present a simplified series and convergence analysis for the setting of second-order polynomial vector fields. The treatment only relies on elementary notions on analytic functions, number theory, and operator norms.     

A diagnostic method for simultaneous feature selection and outlier identification in linear regression

A diagnostic method along the lines of forward search is proposed to simultaneously study the effect of individual observations and features on the inferences made in linear regression. The method operates by appending dummy variables to the data matrix and performing backward selection on the augmented matrix. It outputs sequences of feature-outlier combinations which can be evaluated by plots similar to those of forward search and includes the capacity to incorporate prior knowledge, in order to mitigate issues such as collinearity. It also allows for alternative ways to understand the selection of the final model. The method is evaluated on five data sets and yields promising results.     

Influence functions for a linear subspace method

A linear subspace method, which is one of discriminant methods, was proposed as a pattern recognition method and was studied. Because the method and its extensions do not encounter the situation of singular covariance matrix, we need not consider extensions such as generalized ridge discrimination, even when treating a high dimensional and sparse dataset. In addition, classifiers based on a multi-class discrimination method can function faster because of the simple decision procedure. Therefore, they have been widely used for face and speech recognition. However, it seems that sufficient studies have not been conducted about the statistical assessment of training data performance for classifier in terms of prediction accuracy. In statistics, influence functions for statistical discriminant analysis were derived and the assessments for analysis result were performed. These studies indicate that influence functions are useful for detecting large influential observations for analysis results by using discrimination methods and they contribute to enhancing the performance of a target classifier.