Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions

The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.

2D Minimum Compliance Topology Optimization Based on a Region Partitioning Strategy

This paper presents an extended sequential element rejection and admission(SERA)topology optimizationmethod with a region partitioning strategy.Based on the partitioning of a design domain into solid regions and weak regions,the proposed optimizationmethod sequentially implements finite element analysis(FEA)in these regions.After standard FEA in the solid regions,the boundary displacement of the weak regions is constrained using the numerical solution of the solid regions as Dirichlet boundary conditions.This treatment can alleviate the negative effect of the material interpolation model of the topology optimization method in the weak regions,such as the condition number of the structural global stiffness matrix.For optimization,in which the forward problem requires nonlinear structural analysis,a linear solver can be applied in weak regions to avoid numerical singularities caused by the over-deformedmesh.To enhance the robustness of the proposedmethod,the nonmanifold point and island are identified and handled separately.The performance of the proposed method is verified by three 2D minimum compliance examples.

Geometric Condition of 3UPS-S Parallel Mechanism in Singular Configuration

The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.

Stability of GM(1,1) power model on vector transformation

The morbidity problem of the GM（1,1） power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM（1,1） power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM（1,1） power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM（1,1） power model.

Novel high-performance element in the electromagnetic finite-element method——node-edge element

It is known in the computational electromagnetics （CEM） that the node element has a relative wellconditioned matrix, but suffers from the spurious solution problem; whereas the edge element has no spurious solutions, but usually produces an ill-conditioned matrix. Particularly, when the mesh is over dense, the iterative solution of the matrix equation from edge element converges very slowly. Based on the node element and edge element, a node-edge element is presented, which has no spurious solutions and better-conditioned matrix. Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.

Delay and Its Time-derivative Dependent Robust Stability of Uncertain Neutral Systems with Saturating Actuators

This note concerns the problem of the robust stability of uncertain neutral systems with time-varying delay and saturating actuators. The system considered is continuous in time with norm bounded parametric uncertainties. By incorporating the free weighing matrix approach developed recently, some new delay-dependent stability conditions in terms of linear matrix inequalities （LMIs） with some tuning parameters are obtained. An estimate of the domain of attraction of the closed-loop system under a priori designed controller is proposed. The approach is based on a polytopic description of the actuator saturation nonlinearities and the Lyapunov- Krasovskii method. Numerical examples are used to demonstrate the effectiveness of the proposed design method.

On the Preconditioning Properties of RHSS Preconditioner for Saddle-Point Linear Systems

In this paper,for the regularized Hermitian and skew-Hermitian splitting(RHSS)preconditioner introduced by Bai and Benzi(BIT Numer Math 57:287–311,2017)for the solution of saddle-point linear systems,we analyze the spectral properties of the preconditioned matrix when the regularization matrix is a special Hermitian positive semidefinite matrix which depends on certain parameters.We accurately describe the numbers of eigenvalues clustered at(0,0)and(2,0),if the iteration parameter is close to 0.An estimate about the condition number of the corresponding eigenvector matrix,which partly determines the convergence rate of the RHSS-preconditioned Krylov subspace method,is also studied in this work.

Multi-dimensional scenario forecast for generation of multiple wind farms

A novel multi-dimensional scenario forecast approach which can capture the dynamic temporal-spatial interdependence relation among the outputs of multiple wind farms is proposed.In the proposed approach,support vector machine(SVM)is applied for the spot forecast of wind power generation.The probability density function(PDF)of the SVM forecast error is predicted by sparse Bayesian learning(SBL),and the spot forecast result is corrected according to the error expectation obtained.The copula function is estimated using a Gaussian copula-based dynamic conditional correlation matrix regression(DCCMR)model to describe the correlation among the errors.And the multidimensional scenario is generated with respect to the estimated marginal distributions and the copula function.Test results on three adjacent wind farms illustrate the effectiveness of the proposed approach.

ON THE CONSTRUCTION OF WELL-CONDITIONED HIERARCHICAL BASES FOR TETRAHEDRAL H（curl）-CONFORMING NEDELEC ELEMENT

A partially orthonormal basis is constructed with better conditioning properties for tetrahedral H（curl）-conforming Nedelec elements. The shape functions are classified into several categories with respect to their topological entities on the reference 3-simplex. The basis functions in each category are constructed to achieve maximum orthogonaiity. The numerical study on the matrix conditioning shows that for the mass and quasi-stiffness matrices, and in a logarithmic scale the condition number grows linearly vs. order of approximation up to order three. For each order of approximation, the condition number of the quasi-stiffness matrix is about one order less than the corresponding one for the mass matrix. Also, up to order six of approximation the conditioning of the mass and quasi- stiffness matrices with the proposed basis is better than the corresponding one with the Ainsworth-Coyle basis Internat. J. Numer. Methods. Engrg., 58：2103-2130, 2003. except for order four with the quasi-stiffness matrix. Moreover, with the new basis the composite matrix μM ＋ S has better conditioning than the Ainsworth-Coyle basis for a wide range of the parameter μ.

A Well-Conditioned Hierarchical Basis for Triangular H(curl)-Conforming Elements

We construct a well-conditioned hierarchical basis for triangular H(curl)-conforming elements with selected orthogonality.The basis functions are grouped into edge and interior functions,and the later is further grouped into normal and bubble functions.In our construction,the trace of the edge shape functions are orthonormal on the associated edge.The interior normal functions,which are perpendicular to an edge,and the bubble functions are both orthonormal among themselves over the reference element.The construction is made possible with classic orthogonal polynomials,viz.,Legendre and Jacobi polynomials.For both the mass matrix and the quasi-stiffness matrix,better conditioning of the new basis is shown by a comparison with the basis previously proposed by Ainsworth and Coyle[Comput.Methods.Appl.Mech.Engrg.,190(2001),6709-6733].

On the Construction of Well-Conditioned Hierarchical Bases for H(div)-Conforming Rn Simplicial Elements

Hierarchical bases of arbitrary order for H(div)-conforming triangular and tetrahedral elements are constructedwith the goal of improving the conditioning of the mass and stiffness matrices.For the basis with the triangular element,it is found numerically that the conditioning is acceptable up to the approximation of order four,and is better than a corresponding basis in the dissertation by Sabine Zaglmayr[High Order Finite Element Methods for Electromagnetic Field Computation,Johannes Kepler Universit¨at,Linz,2006].The sparsity of the mass matrices from the newly constructed basis and from the one by Zaglmayr is similar for approximations up to order four.The stiffness matrix with the new basis is much sparser than that with the basis by Zaglmayr for approximations up to order four.For the tetrahedral element,it is identified numerically that the conditioning is acceptable only up to the approximation of order three.Compared with the newly constructed basis for the triangular element,the sparsity of the massmatrices fromthe basis for the tetrahedral element is relatively sparser.

A Factor-GARCH Model for High Dimensional Volatilities

This paper proposes a method for modelling volatilities(conditional covariance matrices)of high dimensional dynamic data.We combine the ideas of approximate factor models for dimension reduction and multivariate GARCH models to establish a model to describe the dynamics of high dimensional volatilities.Sparsity condition and thresholding technique are applied to the estimation of the error covariance matrices,and quasi maximum likelihood estimation(QMLE)method is used to estimate the parameters of the common factor conditional covariance matrix.Asymptotic theories are developed for the proposed estimation.Monte Carlo simulation studies and real data examples are presented to support the methodology.

An advanced integrated framework for moving object tracking

This paper first introduces the concept of a geogram that captures richer features to represent the objects. The spatiogram contains some moments upon the coordinates of the pixels corresponding to each bin, while the geogram contains information about the perimeter of grouped regions in addition to features in the spatiogram.Then we consider that a convergence process of mean shift is divided into obvious dynamic and steady states,and introduce a hybrid technique of feature description, to control the convergence process. Also, we propose a spline resampling to control the balance between computational cost and accuracy of particle filtering. Finally, we propose a boosting-refining approach, which is boosting the particles positioned in the ill-posed condition instead of eliminating the ill-posed particles, to refine the particles. It enables the estimation of the object state to obtain high accuracy. Experimental results show that our approach has promising discriminative capability in comparison with the state-of-the-art approaches.