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Nonconvex Differential Variational Inequality and State-Dependent Sweeping Process

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2013年第2期159卷 386-398页

作者： Haddad, Tahar Univ Jijel Fac Sci & Informat Lab Math Pures & Appl Jijel 18000 Algeria

We prove the existence of solutions of a differential variational inequality involving a prox-regular set in an infinite dimensional Hilbert space via a new existence result of a non-convex state-dependent sweeping pr... 详细信息

关键词： Differential variational inequality projection algorithm Prox-regular sets Normal cones

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Global convergence of a non-convex Douglas-Rachford iteration

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第3期57卷 753-769页

作者： Artacho, Francisco J. Aragon Borwein, Jonathan M. Univ Newcastle Ctr Comp Assisted Res Math & Its Applicat CARMA Callaghan NSW 2308 Australia King Abdulaziz Univ Jeddah 21413 Saudi Arabia

We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration Borwein and Sims (Fixed-point algorithms for inverse problems in science and engineering, pp. 93-109, 2011) was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given.

关键词： Non-convex feasibility problem Fixed point theory projection algorithm Douglas-Rachford algorithm Global convergence Signal reconstruction

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Discrete Adaptive Repetitive Control: Convergence Analysis and Implementation

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Acta Automatica Sinica 2013年第4期39卷 400-406页

作者： Ming-Xuan SUN Lin-Jiang YU Hai-Gang HE College of Information Engineering Zhejiang University of Technology Hangzhou 310023 China

This paper presents an adaptive repetitive control method for discrete periodically time-varying systems with known periodicity. When estimating unknowns, a repetitive learning projection algorithm with dead-zone is used. The result in this paper can be considered an application of the key technique lemma in repetition domain, by which stability and convergence of the discrete adaptive repetitive control system are established. It is shown that both system input and output are bounded and the tracking error would converge to the bound on the disturbance variable. A linear motor servo system is taken as an example, and experiment results are presented for demonstrating effectiveness of the proposed method.

关键词： Adaptive repetitive control projection algorithm dead-zone modification discrete-time periodic systems

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A Bi-level Formulation for the Combined Dynamic Equilibrium based Traffic Signal Control

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Procedia - Social and Behavioral Sciences 2013年 80卷 729-752页

作者： Satish Ukkusuri Kien Doan H.M. Abdul Aziz School of Civil Engineering Purdue University West Lafayette Indiana 47907–2051

This paper formulates the combined dynamic user equilibrium and signal control problem (DUESC) as a bi-level optimization problem. The signal control operator in the upper level optimizes the signal setting to minimize the system travel time whereas the road users in the lower level minimize their own costs (by changing departure times, paths or both) leading to dynamic user equilibrium behavior. Three components of the bi-level formulation are discussed including network loading model, the dynamic user equilibrium model and the signal control model. Then the combined problems are formulated as a Nash-Cournot game and a Stackelberg game. A solution technique based on the iterative optimization and assignment (IOA) method is proposed to solve the DUESC problem. We use the projection algorithm to solve the lower level and the mixed integer programming solver to solve the upper level. Extensive numerical results demonstrate the benefits of using this model.

关键词： Dynamic user equilibrium Signal control optimization Nash-Cournot game Stackelberg game Mixed integer program projection algorithm

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Adaptive Position Control with Using a Smooth projection Adaptation Law for 2 DOF Flexible Link Robot Arm

Adaptive Position Control with Using a Smooth Projection Ada...

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Annual Conference of the Society-of-Instrument-and-Control-Engineers (SICE)

作者： Sawada, Masataka Itamiya, Keietsu Natl Def Acad Dept Elect & Elect Engn Yokosuka Kanagawa 2398686 Japan

ISBN: (纸本)9784907764401

We have already proposed high order tuner (HOT) which uses a smooth projection algorithm to ensure the positive definiteness of an estimated inertia matrix for realizing a stability and a good transient response of adaptive tracking control system based on [7] for a rigid link robot arm. Also, we proposed a HOT capable to constrain adjustable parameters into hyper-parallelogram region [8, 9]. In this paper, an adaptive control scheme for a 2 DOF flexible link robot arm is proposed. The controller is composed of an adaptation law using smooth projection algorithm [8, 9] and a control law based on dynamic certainty equivalent principle [7, 14]. The effectiveness of the proposed scheme is illustrated by a theoretical analysis and simple numerical simulation results.

关键词： adaptive control flexible link robot arm computed torque method projection algorithm

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Frequency determination in control applications: excitation-based approach

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2012年第I8期226卷 1142-1148页

作者： Stotsky, Alexander Chalmers Univ Technol Dept Signals & Syst SE-41296 Gothenburg Sweden

New algorithms for estimation of the frequencies of oscillating waveform signals are described. A model of the signals is presented in the form of a linear difference equation with unknown coefficients, which define the frequencies and amplitudes. Coefficients are estimated utilizing the property of the persistence of excitation of oscillating signals. Exponentially damped and oscillating signals are described in a unified framework. A property of excitation is proved for an exponentially damped signal that contains a single frequency via diagonal dominance of an information matrix. Two applications of this frequency estimation technique are considered. The first one is filtering of the wind speed signal in wind turbine control applications, and the second one is the frequency estimation of exponentially damped signals motivated by the engine knock detection applications.

关键词： Frequency estimation persistence of excitation strictly diagonally dominant matrix exponentially damped signal projection algorithm wind speed model engine knock frequency

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A convergence result on random products of mappings in metric spaces

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FIXED POINT THEORY AND APPLICATIONS 2012年第1期2012卷 1-7页

作者： Khamsi, Mohamed Amine Louhichi, Issam Univ Texas El Paso Dept Math Sci El Paso TX 79968 USA King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

Let be a metric space and {T-1, ..., T-N} be a finite family of mappings defined on D subset of X. Let r: N -> {1,..., N} be a map that assumes every value infinitely often. The purpose of this article is to establish the convergence of the sequence (x(n)) defined by x(0) is an element of D;and x(n+1) = T-r(n)(x(n)), for all n >= 0. In particular, we extend the study of Bauschke [1] from the linear case of Hilbert spaces to metric spaces. Similarly we show that the examples of convergence hold in the absence of compactness. These type of methods have been used in areas like computerized tomography and signal processing.

关键词： computerized tomography convex feasibility problem convex programming Fejer monotone sequence image reconstruction image recovery innate bounded regularity Kaczmarz's method nonexpansive mapping projection algorithm projective mapping random product signal processing unrestricted iteration unrestricted product'

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A convergence result on random products of mappings in metric trees

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FIXED POINT THEORY AND APPLICATIONS 2012年第1期2012卷 1-10页

作者： Al-Mezel, Saleh Abdullah Khamsi, Mohamed Amine King Abdulaziz Univ Dept Math Jeddah 21589 Saudi Arabia Univ Texas El Paso Dept Math Sci El Paso TX 79968 USA

Let X be a metric space and {T (1), ..., T (N) } be a finite family of mappings defined on D aS, X. Let r : a"center dot -> {1,..., N} be a map that assumes every value infinitely often. The purpose of this article is to establish the convergence of the sequence (x (n) ) defined by x(0) is an element of D;and x(n+1) = T-r(n)(x(n)), for all n >= 0. In particular we prove Amemiya and Ando's theorem in metric trees without compactness assumption. This is the first attempt done in metric spaces. These type of methods have been used in areas like computerized tomography and signal processing.

关键词： computerized tomography convex feasibility problem convex programming metric tree nonexpansive mapping projection algorithm projective mapping random product signal processing unrestricted iteration unrestricted product

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Field depth extension of 2D barcode scanner based on wavefront coding and projection algorithm

Field depth extension of 2D barcode scanner based on wavefro...

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Conference on Information Optics and Photonics Technologies II

作者： Zhao Tingyu Zi, Ye Zhang Wenzi Huang Weiwei Yu Feihong Zhejiang Univ Dept Opt Engn State Key Lab Modern Opt Instrumentat Hangzhou 310027 Peoples R China

ISBN: (纸本)9780819470126

Wavefront coding (WFC) used in 2D barcode scanners can extend the depth of field into a great extent with simpler structure compared to the autofocus microscope system. With a cubic phase mask (CPM) employed in the STOP, blurred images will be obtained in charge coupled device (CCD), which can be restored by digital filters. Direct methods are used widely in real-time restoration with good computational efficiency but with details smoothed. Here, the results of direct method are firstly filtered by hard-threshold function. The positions of the steps can be detected by simple differential operators. With the positions corrected by projection algorithm, the exact barcode information is restored. A wavefront coding system with 7mm effective focal length and 6 F-number is designed as an example. Although with the different magnification, images of different object distances can be restored by one point spread function (PSF) with 200mm object distance. A QR code (Quickly Response Code) of 31mm X 27mm is used as a target object. The simulation results showed that the sharp imaging objective distance is from 80mm to 355mm. The 2D barcode scanner with wavefront coding extends field depth with simple structure, low cost and large manufacture tolerance. This combination of the direct filter and projection algorithm proposed here could get the exact 2D barcode information with good computational efficiency.

关键词： 2D barcode scanner field depth extension wavefront coding projection algorithm

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Method of Hybrid Multi-attribute Decision Making Based on Relative Entropy Weight and projection algorithm

Method of Hybrid Multi-attribute Decision Making Based on Re...

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7th World Congress on Intelligent Control and Automation

作者： Rao, Congjun Peng, Jin Zhang, Zhongcheng Huanggang Normal Univ Coll Math & Informat Sci Huanggang 438000 Hubei Peoples R China

ISBN: (纸本)9781424421138

The problem of hybrid multi-attribute decision making, which integrates with interval numbers and linguistic fuzzy numbers, and incomplete information on attribute weights, is studied. Based on the relative entropy weight and projection algorithm, a new method of hybrid multi-attribute decision making is presented. First of all, the definitions of closeness degree and relative entropy are given, and the method of transforming the interval numbers and linguistic fuzzy numbers into triangular fuzzy numbers is presented. Secondly, by solving a set of linear programming models whose goals are to maximize the closeness degree, a series of preference weight vectors which are partial for each alternative are obtained, and then the optimal weight vector is got by aggregating the preference weight vectors through establishing a relative entropy weight model. Thirdly, based on this optimal weight vector, the projection algorithm is presented to rank order for all alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new method.

关键词： Hybrid multi-attribute decision making Relative entropy weight Closeness degree projection algorithm

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