A Chebyshev Finite Difference Method For Solving A Class Of Optimal Control Problems

A new Chebyshev finite difference method for solving class of optimal control problem is proposed. The algorithm is based on Chebyshev approximations of the derivatives arising in system dynamics. In the performance index, we use Chebyshev approximations for integration. The numerical examples illustrate the robustness, accuracy and efficiency of the proposed technique.     

The mise en scéne of memristive networks: effective memory,dynamics and learning

Abstract

We discuss the properties of the dynamics of purely memristive circuits using a recently derived consistent equation for the internal memory variables of the involved memristors. In particular, we show that the number of independent memory states in a memristive circuit is constrained by the circuit conservation laws, and that the dynamics preserves these symmetry by means of a projection on the physical subspace. Moreover, we discuss other symmetries of the dynamics under various transformations of the involved variables, and study the weak and strong non-linear regimes of the dynamics. In the strong regime, we derive a conservation law for the internal memory variable. We also provide a condition on the reality of the eigenvalues of Lyapunov matrices. The Lyapunov matrix describes the dynamics close to a fixed point, for which show that the eigenvalues can be imaginary only for mixtures of passive and active components. Our last result concerns the weak non-linear regime, showing that the internal memory dynamics can be interpreted as a constrained gradient descent, and provide the functional being minimized. This latter result provides another direct connection between memristors and learning.     

Observation and output adaptive tracking for a class of nonlinear non-minimum phase systems

ABSTRACT

In this paper, the output tracking problem for a class of systems with unstable zero dynamics is addressed. The state is assumed not measurable. The output of the dynamical system to be controlled has to track a signal, which is the sum of a known number of sinusoids with unknown frequencies, amplitudes and phases. The non-minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods, which are known to generate unstable behaviours of the internal dynamics. The proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state; therefore, a nonlinear observer is needed. Due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states, adaptive indirect methods are applied.     

英文字母特征的双面碎纸拼接

目的 结合图像处理技术和英文字母特征,提出一种基于聚类和全局优化的双面碎纸拼接复原算法.方法 利用图像处理技术,消除同行字母的处于不同高度部分.再分别基于处理前后的碎纸片,分别提出碎片与行之间匹配程度以及刻画相邻碎片两两匹配的特征参数(像素差与相关系数).利用上述两特征参数,将问题转化为两个子优化问题:子问题1,基于像素差的最大值最小目标,建立全局最优聚类模型,确定所有碎片的行分类;子问题2,将同一行中相邻碎片的匹配问题转化为旅行商问题(TSP),并基于相关系数对每一行建立全局优化模型.结果 仿真实验结果表明,图像处理技术能有效地消除同行字母处于不同高度的负影响.同时,获取的两个特征参数能很好地刻画碎片之间的匹配,复原准确率达到90％以上.结论 实验结果表明,该算法能保证高复原率且降低复杂度,对碎纸机碎纸拼接复原具有良好的实际意义.     

Study on Roller-Walker — Improvement of Locomotive Efficiency of Quadruped Robots by Passive Wheels

Abstract

Roller-Walker is a leg–wheel hybrid mobile robot using a passive wheel equipped on the tip of each leg. The passive wheel can be transformed into sole mode by rotating the ankle roll joint when Roller-Walker walks on a rough terrain. This paper discusses the energy efficiency of locomotion in wheeled mode. We define a leg trajectory to produce forward straight propulsion, and discuss the relationships between the parameters of the leg trajectory and energy efficiency of the propulsion using a dynamics simulator. We find optimum parameter sets where optimization criterion is specific resistance. The results indicate that faster locomotion achieves higher energy efficiency. We then carry out hardware experiments and empirically derive the experimental specific resistance. We show that wheeled locomotion has an 8-times higher energy efficiency than the ordinary crawl gait. Finally, we compare the specific resistance of Roller-Walker with other walking robots described in the literature.     

A modified infeasible interior-point algorithm with full-Newton step for semidefinite optimization

ABSTRACT

Recently, Mansouri et al. (J. Optim. Theory Appl. 166: 605-618, 2015) presented an improved infeasible interior-point algorithm for linear optimization. Their algorithm has the shortcoming that the proximity measure may be still large when the duality gap approaches to zero. In this paper, we propose an infeasible interior-point algorithm for semidefinite optimization with a modified search direction. This modification is an attempt to decrease the value of the proximity measure, which is important to determine whether or not to perform centreing steps in the classical infeasible interior-point algorithms. Some preliminary numerical results show the benefit of the proposed algorithm as well.     

Linear scaling first-principles molecular dynamics with controlled accuracy

In our quest for accurate linear scaling first-principles molecular dynamics methods for pseudopotential DFT calculations, we investigate the accuracy of real-space grid approaches, with finite differences and spherical localization regions. We examine how the positions of the localization centers affect accuracy and the convergence rate in the optimization process. In particular we investigate the accuracy of the atomic forces computation compared to the standard O(N³) approach. We show the exponential decay of the error on the energy and forces with the size of the localization regions for a variety of realistic physical systems. We propose a new algorithm to automatically adapt the localization centers during the ground state computation which allows for molecular dynamics simulations with diffusion processes. The combination of algorithms proposed lead to a genuine linear scaling First-Principles Molecular Dynamics method with controlled accuracy. We illustrate our approach with examples of microcanonical molecular dynamics with localized orbitals.     

An algebraic transformation framework for multidatabase queries

Existence of semantic conflicts between component databases severely impacts query processing in a multidatabase system. In this paper, we describe two types of semantic conflicts that have to be dealt with in the integration of databases modeling information about related sets of real-world entities. These are the entityidentification problem and theattribute value conflict problem. While thetwo-way outerjoin operation has been commonly used for resolving entity identification problem between two component relations, outerjoins using regular equality comparisons between component relation keys is shown to produce counter-intuitive entity identification result. We remedy this by defining a newkey-equality comparator in place of regular equality comparator, for outerjoins. For the attribute value conflict problem, we define aGeneralized Attribute Derivation (GAD) operation which allows user-defined attribute derivation functions to be used to compute new attributes from the component relations' attributes. By adding two-way outerjoin andGAD to the set of relational operations, the traditional algebraic transformation framework for relational queries is no longer adequate for multidatabase query processing and optimization. As a result, we introduceconstrained query tree as the multidatabase query representation. We show that some knowledge about query predicates and attribute derivation functions can be used to simplify queries. Such knowledge is modeled as an outerjoin graph attached to every outerjoin operation in the query tree. Based on this, we further extend the traditional algebraic transformation framework to include two-way outerjoins andGAD operations. Our framework demonstrates that properties of selection/join predicates and attribute derivation functions can be used to provide interesting transformation alternatives. This framework also serves as a formal ground for developing optimization strategies for multidatabase queries. Recommended by: Clement Yu     

A Comparative Study Of Global Optimization Approaches To Meg Source Localization

It is well-known that the problem of MEG source localization can be cast as an optimization problem. So far, there have been many works in which various optimization methods were adopted for source localization. In this paper, we compare the performance of three typical and widely used optimization techniques for a specific MEG source localization problem. We first introduce a hybrid algorithm by combining genetic and local search strategies to overcome disadvantages of conventional genetic algorithms. Second, we apply the tabu search, a widely used optimization method in combinational optimization and discrete mathematics, to source localization. To the best of our knowledge, this is the first attempt in the literature to apply tabu search to MEG/EEG source localization. Third, in order to further compare the performance of the above algorithms, simulated annealing is also applied to MEG source localization problem. The computer simulation results show that our local genetic algorithm is the most effective approach to dipole localization, and the tabu search method is also a very good strategy for this problem.     

Global stability of a discrete virus dynamics model with diffusion and general infection function

ABSTRACT

We investigate a discrete virus dynamics model with diffusion and general infection function. For this model, we derive the basic reproduction number and show the global stability of the equilibria. Example and numerical simulation are performed to illustrate the theoretical results.     

Isogeometric analysis in option pricing

ABSTRACT

Isogeometric analysis is a recently developed computational approach that integrates finite element analysis directly into design described by non-uniform rational B-splines (NURBS). In this paper, we show that price surfaces that occur in option pricing can be easily described by NURBS surfaces. For a class of stochastic volatility models, we develop a methodology for solving corresponding pricing partial integro-differential equations numerically by isogeometric analysis tools and show that a very small number of space discretization steps can be used to obtain sufficiently accurate results. Presented solution by finite element method is especially useful for practitioners dealing with derivatives where closed-form solution is not available.     

Development of a Sensor Fusion Strategy for Robotic Application Based on Geometric Optimization

Fusion of multi-sensor information is an important technology, which is growing exponentially due to its tremendous application potential in many areas. Effective fusion of data from sensors is very critical in increasing an intelligent system's capability to accomplish complex tasks. Appropriate fusion technologies are needed to be developed specially when a system requires redundant sensors to be used. More the redundancy in sensors, more is the computational complexity for controlling the system and more is its intelligence level. This research presents a strategy developed for multiple sensor fusion, based on geometric optimization. Each sensor's uncertainty has been modeled using classical Lagrangian optimization techniques. However, the uniqueness and effectiveness of the present technique lies on the fact that starting from the optimized value as initial estimate the accuracy of the sensory information has further been improved up to any pre defined bounded range, by developing two architectures – FFA (fission–fusion architecture) and FDD (fusion in differential domain). Sufficient evidences and analyses have been provided in the paper to show its effectiveness in various applications.     

Symmetric rank-1 approximation of symmetric high-order tensors

ABSTRACT

Finding the symmetric rank-1 approximation to a given symmetric tensor is an important problem due to its wide applications and its close relationship to the Z-eigenpair of a tensor. In this paper, we propose a method based on the proximal alternating linearized minimization to directly solve the optimization problem. Global convergence of our algorithm is established. Numerical experiments show that our algorithm is very competitive in speed, accuracy and robustness compared to other state-of-the-art methods.     

小物体3维重建中影像与几何模型的配准

目的 近景摄影测量中的目标几何形状复杂,且拍摄影像的角度变化大,给影像与几何模型的配准带来了困难。传统单幅影像与几何模型配准的做法,由于缺乏自动粗配准的方法,效率相对较低。将多视影像首先统一坐标系的做法,在近景目标的复杂背景下也难以实现。方法 为此,将近景目标置于平面标定板上,利用相机标定的方法同时解算出影像的内外方位元素,实现多视影像坐标系的统一。然后人工选取3组以上同名点,做多视影像与几何模型的绝对定向,得到初始配准参数。最后使用多视影像与几何模型漫反射渲染图之间的归一化互信息作为相似性测度,用Powell非线性优化方法得到配准参数的精确值。结果 实验结果表明,使用标定板可以稳定地获取多视影像的内外方位元素,用绝对定向得到的配准参数进行影像和几何模型的交替显示仍然可以看到明显的裂缝,在经过互信息优化后裂缝现象得到明显改善。结论 多视影像与几何模型配准相比传统单幅影像与几何模型配准,人工选取同名点的工作量大大减少,由于人工选点存在误差,影响绝对定向的精度,使用归一化互信息作为测度进行非线性优化,可以获得更高的精度。     

The Multifactor Nature of the Volatility of Futures Markets

This paper estimates a model of interest rate dynamics containing multi-factor Wiener and single-factor Poisson jump volatility components. Data from the highly liquid but short term futures markets are used. The difficult numerical problem of estimating such multi-factor models is resolved by using a genetic algorithm to carry out the optimization procedure. It is established that the multi-factor Wiener volatility components are adequate to model the interest rate dynamics without the need to incorporate Poisson jump components, the existence of which would create difficulties in the practical use of interest rate models. Jel Classification No: C51, C61, E43     

Shape and topology optimization for periodic problems

The present paper deals with the implementation of an optimization algorithm for periodic problems which alternates shape and topology optimization; the theoretical background about shape and topological derivatives was developed in Part I (Barbarosie and Toader, Struct Multidiscipl Optim, 2009). The proposed numerical code relies on a special implementation of the periodicity conditions based on differential geometry concepts: periodic functions are viewed as functions defined on a torus. Moreover the notion of periodicity is extended and cases where the periodicity cell is a general parallelogram are admissible. This approach can be adapted to other frameworks (e.g. Bloch waves or fluid dynamics). The numerical method was tested for the design of periodic microstructures. Several examples of optimal microstructures are given for bulk modulus maximization, maximization of rigidity for shear response, maximization of rigidity in a prescribed direction, minimization of the Poisson coefficient.     

A flexible cluster-oriented alternative clustering algorithm for choosing from the Pareto front of solutions

Supervised alternative clustering is the problem of finding a set of clusterings which are of high quality and different from a given negative clustering. The task is therefore a clear multi-objective optimization problem. Optimizing two conflicting objectives at the same time requires dealing with trade-offs. Most approaches in the literature optimize these objectives sequentially (one objective after another one) or indirectly (by some heuristic combination of the objectives). Solving a multi-objective optimization problem in these ways can result in solutions which are dominated, and not Pareto-optimal. We develop a direct algorithm, called COGNAC, which fully acknowledges the multiple objectives, optimizes them directly and simultaneously, and produces solutions approximating the Pareto front. COGNAC performs the recombination operator at the cluster level instead of at the object level, as in the traditional genetic algorithms. It can accept arbitrary clustering quality and dissimilarity objectives and provides solutions dominating those obtained by other state-of-the-art algorithms. Based on COGNAC, we propose another algorithm called SGAC for the sequential generation of alternative clusterings where each newly found alternative clustering is guaranteed to be different from all previous ones. The experimental results on widely used benchmarks demonstrate the advantages of our approach.

     

区域拟合的背景去除图像分割模型

目的 图像分割是图像处理领域的重要研究内容之一,且应用广泛。在基于PDE和变分法的图像分割方法中,大部分图像分割模型的能量泛函均为非凸性,较容易陷入局部极小解,因而分割结果往往不尽如人意,且运算时间较慢。为此,本文根据背景去除模型的思想结合区域拟合的方法,提出了一种区域拟合的背景去除图像分割模型。方法 首先对背景去除模型进行改造;再结合区域拟合的方法对模型进行改进,并对改进模型进行凸优化处理;最后结合水平集和Split Bregman法对改进模型进行快速求解,获得全局最小值解。结果 针对改进模型在分割效果、计算效率及初始化位置对实验结果的影响这3个方面了进行数值实验,相较于ICV(improved Chan-Vese)模型、LK(Li-Kim)模型及CV(Chan-Vese)模型,本文模型能得到更优的分割效果,且在分割效果相似的情况下,本文模型较RSF(region-scalable fitting)模型耗时更短,同时当实验初始化位置不同时,实验亦能取得良好的分割效果。结论 在对于MRI(magnetic resonance imaging)图像以及合成图像等进行处理时,本文所给出的模型不仅能获得良好的分割效果,并且效率较高,而且从实验结果来看,本文模型具有一定的鲁棒性。     

Semantic segmentation of trajectories with improved agent models for pedestrian behavior analysis

ABSTRACT

In this paper, we propose a method for semantic segmentation of pedestrian trajectories based on pedestrian behavior models, or agents. The agents model the dynamics of pedestrian movements in two-dimensional space using a linear dynamics model and common start and goal locations of trajectories. First, agent models are estimated from the trajectories obtained from image sequences. Our method is built on top of the Mixture model of Dynamic pedestrian Agents (MDA); however, the MDA's trajectory modeling and estimation are improved. Then, the trajectories are divided into semantically meaningful segments. The subsegments of a trajectory are modeled by applying a hidden Markov model using the estimated agent models. Experimental results with a real trajectory dataset show the effectiveness of the proposed method as compared to the well-known classical Ramer-Douglas-Peucker algorithm and also to the original MDA model.