Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an outputdependent switching law by constructing a robust Luenberger observer for each subsystem.

Addendum to: An Approach to Hierarchical Clustering via Level Surfaces and Convexity

This article is an addendum to the 2001 paper [1] which investigated an approach to hierarchical clustering based on the level sets of a density function induced on data points in a d-dimensional feature space. We refer to this as the “level-sets approach” to hierarchical clustering. The density functions considered in [1] were those formed as the sum of identical radial basis functions centered at the data points, each radial basis function assumed to be continuous, monotone decreasing, convex on every ray, and rising to positive infinity at its center point. Such a framework can be investigated with respect to both the Euclidean (L2) and Manhattan (L1) metrics. The addendum here puts forth some observations and questions about the level-sets approach that go beyond those in [1]. In particular, we detail and ask the following questions. How does the level-sets approach compare with other related approaches? How is the resulting hierarchical clustering affected by the choice of radial basis function? What are the structural properties of a function formed as the sum of radial basis functions? Can the levels-sets approach be theoretically validated? Is there an efficient algorithm to implement the level-sets approach?

Martingales and Super-Martingales Relative to a Convex Set of Equivalent Measures

In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The description of all local regular super-martingales relative to a convex set of equivalent measures is presented. The notion of the complete set of equivalent measures is introduced. We prove that every bounded in some sense super-martingale relative to the complete set of equivalent measures is local regular. A new definition of the fair price of contingent claim in an incomplete market is given and the formula for the fair price of Standard Option of European type is found. The proved Theorems are the generalization of the famous Doob decomposition for super-martingale onto the case of super-martingales relative to a convex set of equivalent measures.

RADIAL CONVEX SOLUTIONS OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE

In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theorem in cones. We deal with more general nonlinear term than those in the literature.

SHARP ESTIMATES OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α

In this paper,we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order a on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis.Then,as the application of these sharp inequalities,we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk U^n in C^n.

结构鲁棒优化的非概率集合理论凸方法

以传统的优化理论为基础,考虑含不确定结构参数的情况,提出了非概率凸集合理论的结构优化方法. 将结构优化列式中的目标函数与约束条件所含有的不确定参数用凸集合定量化,只需知道其所在范围的边界, 降低了以往处理不确定性问题概率方法需要知道不确定参数的均值、方差或概率分布密度等详细统计信息的要求.提出的鲁棒优化方法在使目标函数达到设计要求的同时,结构还能承受结构参数在其所在范围内变化引起结构性能的变异.通过优化问题中普遍使用的10杆平面桁架和一个72杆空间桁架实例,给出了当结构参数为名义值时结构的优化结果,以及结构参数具有不确定性时的优化结果,力求表明所介绍的方法的可行性和优越性.

负荷分配问题的最陡增/减变量对寻优法

机组的经济目标函数以多段或二次项系数小于零的单段二次函数表示时,负荷分配问题就呈现出非凸、非线性特性,给高效求取全局最优解或具有较高性能的局部最优解带来了较大困难。该文提出了一种最陡增/减变量对寻优法,此方法每次迭代过程只有两个变量(变量对)发生变化,其中一个增大,另一个进行同等量值的减小,增/减的步长按照一定的规则动态控制,并确保满足约束条件;同时,从原目标函数关于增/减变量对的偏导数和最小的变量对中动态地选择变量对,以确保每次迭代都能够按照使原目标函数最陡下降的变量对方向进行。此方法可快速求得凸二次规划问题的全局最优解和非凸二次规划问题的局部最优解。进一步地,该文结合问题的特点引入一种简捷的进化策略,使最陡增/减变量对寻优法在进化规划的框架下获得了能够求得非凸二次规划问题全局最优解的能力,并在很大程度上保留了原方法快速寻优的优点。算例表明,该文方法和策略为非凸二次规划负荷分配问题提供了一种高效实用的分析工具。

Computer Aided Design Technology for Convex Faceted Gem Cuts Based on the Half-Edge Data Structure

Aiming to increase the efficiency of gem design and manufacturing, a new method in computer-aided-design (CAD) of convex faceted gem cuts (CFGC) based on Half-edge data structure (HDS), including the algorithms for the implementation is presented in this work. By using object-oriented methods, geometrical elements of CFGC are classified and responding geometrical feature classes are established. Each class is implemented and embedded based on the gem process. Matrix arithmetic and analytical geometry are used to derive the affine transformation and the cutting algorithm. Based on the demand for a diversity of gem cuts, CAD functions both for free-style faceted cuts and parametric designs of typical cuts and visualization and human-computer interactions of the CAD system including two-dimensional and three-dimensional interactions have been realized which enhances the flexibility and universality of the CAD system. Furthermore, data in this CAD system can also be used directly by the gem CAM module, which will promote the gem CAD/CAM integration.

A Family of Non-Self Maps Satisfying <i>Φ</i>_i-Contractive Condition and Having Unique Common Fixed Point in Metrically Convex Spaces

Class of 5-dimensional functions Φ was introduced and a convergent sequence determined by non-self mappings satisfying certain Φi-contractive condition was constructed, and then that the limit of the sequence is the unique com-mon fixed point of the mappings was proved. Finally, several more general forms were given. Our main results gener-alize and unify many same type fixed point theorems in references.

NEW HYBRID CONJUGATE GRADIENT METHOD AS A CONVEX COMBINATION OF LS AND FR METHODS

In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn't depend on any line search. Next, we also prove that, moduling the value of the parameter t,the Newton direction condition is equivalent to Dai-Liao conjugacy condition.The strong Wolfe line search conditions are used.The global convergence of this new method is proved.Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one.

Continuous Iteratively Reweighted Least Squares Algorithm for Solving Linear Models by Convex Relaxation

In this paper, we present continuous iteratively reweighted least squares algorithm (CIRLS) for solving the linear models problem by convex relaxation, and prove the convergence of this algorithm. Under some conditions, we give an error bound for the algorithm. In addition, the numerical result shows the efficiency of the algorithm.

Generalized Quasi Variational-Type Inequalities

In this paper, we define the concepts of (η,h)-quasi pseudo-monotone operators on compact set in locally convex Hausdorff topological vector spaces and prove the existence results of solutions for a class of generalized quasi variational type inequalities in locally convex Hausdorff topological vector spaces.

Higher-Order Minimizers and Generalized (F,<i>ρ</i>)-Convexity in Nonsmooth Vector Optimization over Cones

In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.

An Introduction to Convex Optimization Theory in Communication Signals Recognition

In this paper,convex optimization theory is introduced into the recognition of communication signals. The detailed content contains three parts. The first part gives a survey of basic concepts,main technology and recognition model of convex optimization theory. Special emphasis is placed on how to set up the new recognition model of communication signals with multisensor reports. The second part gives the solution method of the recognition model,which is called Logarithmic Penalty Barrier Function. The last part gives several numeric simulations,in contrast to D-S evidence inference method,this new method can also generate reasonable recognition results. Moreover,this new method can deal with the form of sensor reports which is more general than that allowed by the D-S evidence inference method,and it has much lower computation complexity than that of D-S evidence inference method. In addition,this new method has better recognition result,stronger anti-interference and robustness. Therefore,the convex optimization methods can be widely used in the recognition of communication signals.

Multicut L-Shaped Algorithm for Stochastic Convex Programming with Fuzzy Probability Distribution

Two-stage problem of stochastic convex programming with fuzzy probability distribution is studied in this paper. Multicut L-shaped algorithm is proposed to solve the problem based on the fuzzy cutting and the minimax rule. Theorem of the convergence for the algorithm is proved. Finally, a numerical example about two-stage convex recourse problem shows the essential character and the efficiency.

A novel method for virtual clearance computation of high-speed train based on model integration and convex hull

The 3D clearance of a high-speed train(HST) is critical to ensure the safety of railway transportation. Many studies have been conducted on the inspection of the clearance profile in railway operation based on the vision system, but few researchers have focused on the computation of the 3D clearance in the design phase of an HST. This paper summarizes the virtual 3D clearance computation of an HST based on model integration and the convex hull method. First, both the aerodynamic and kinetic analysis models of the HST are constructed. The two models are then integrated according to the corresponding relationship map, and an array of transformation matrixes of the HST is created to drive the designed model simulating the physical railway motion. Furthermore, the convex hull method is adopted to compute the 3D envelope of the moving train. Finally, the Hausdorff metric is involved in the measurement of the minimum clearance model and the 3D envelope model. In addition, the color map of the Hausdorff distance is established to verify that the designed shape of the HST meets the national standards. This paper provides an effective method to accurately calculate the 3D clearance for the shape design of an HST, which greatly reduces the development cost by minimizing the physical prototype that must be built.

On the Convexity of Generalized Grotzsch Ring Function

In this paper,the authors study the monotoneity and convexity of certain combinations and composites defined in terms of the generalized Grotzsch ring function μa (r), which appears in Ramanujan' s generalized modular equations,and obtain some inequalities for this function.

Effects of the Convex Topography on Railway Environmental Vibrations

The railway environmental vibration caused by high-speed railways is harmful to the human health,the structural safety of adjacent buildings,and the normal use of precision instruments.At the same time,it occurs frequently.In this case,the railway environmental vibration has drawn much attention with the rapid development of highspeed railways.Studies in Earthquake Engineering show that a convex topography has a great impact on ground vibrations,however,there is no consideration about the convex topographic effect in the study of the railway environmental vibration when the convex topography is near the roadway.In this paper,the influence of a convex topography on the railway environmental vibration was investigated.Two-dimensional(2D)finite element models consist of subgrade-convex topography and subgrade-flat topography are established using the finite element method.The length and the height of the analysis model are taken as 200 m and 41.3 m,respectively.The external soil of the calculation model is simulated via the artificial boundary.By comparison with measured results,the 2D finite element models were verified to be effective.The convex topographic effect is studied by conducting parameter investigations,such as the bottom width,cross-sectional shape,height-width ratio and the foundation soil properties.Results show that the dimension and cross-section shape of the convex topography and the foundation soil properties have significant effect on the convex topographic effect.

A New Heuristic for the Convex Quadratic Programming Problem

This paper presents a new heuristic to linearise the convex quadratic programming problem. The usual Karush-Kuhn-Tucker conditions are used but in this case a linear objective function is also formulated from the set of linear equations and complementarity slackness conditions. An unboundedness challenge arises in the proposed formulation and this challenge is alleviated by construction of an additional constraint. The formulated linear programming problem can be solved efficiently by the available simplex or interior point algorithms. There is no restricted base entry in this new formulation. Some computational experiments were carried out and results are provided.

机器设计选择、工程平衡及Convex C2系列的决策过程

计算机界普遍认为,计算机结构还没有形成一种科学,只是一种工艺,至多在某些部分可称为科学,大部分只是一种科学的方法。从广义上讲计算机重要的不是发明什么,而是要形成一种别人肯买它的产品。买的人越多,应用就越广;应用越广,它本身的改进也就越快。在开始设计一种新机器时,必须要考虑到预算,元器件的现状水平,需要消耗多少人年,技术的提前量与实际实施的可能性等综合因素,在诸多因素中力求取得最佳平衡点。由于我们只考虑机器本身,故在此不考虑市场前景等非技术性的因素。