H∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay

In this paper, H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H1 state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.     

Three-dimensional analysis of Marangoni flow and radial segregation in Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript> melt with Czochralski configuration

In order to examine the flow field and the radial segregation of silicon (Si) in a Ge _x Si_1-x melt with an idealized Czochralski (Cz) configuration, we conducted a series of unsteady three-dimensional (3-D) numerical simulations under zero-gravity conditions. The effect of convection driven by surface tension on the free surface of the melt was included in the model, by considering thermal, as well as solutal Marangoni convection. The concentration and flow fields at several stages during crystal growth are presented for several temperature differences, driving the Marangoni convection. The simulation results indicate that the flow and concentration fields are axisymmetric for Ma _T < 625 and become oscillatory and 3-D for higher values. It was found that the maximum Si concentration difference at the growth interface decreases as thermal Marangoni number increases due to higher flow velocities in the vicinity of the interface. However, temporal fluctuations of Si concentration at the interface increase at higher thermal Marangoni numbers. The effects of aspect ratio (A _r) were also considered in the model. It was found that the aspect ratio of the melt in the crucible has a prominent influence on the flow pattern in the melt which, in turn, effects the Si concentration at the growth interface.     

Intuitionistic (<Emphasis Type="Italic">S</Emphasis>, <Emphasis Type="Italic">T</Emphasis>)-fuzzy hyperquasigroups

The concept of intuitionistic fuzzy subhyperquasigroups in a hyperquasigroup with respect to an s-norm and a t-norm on intuitionistic fuzzy sets is introduced and their properties of such hyperquasigroups are studied. Intuitionistic (S, T)-fuzzy relations on a hyperquasigroup G are discussed. In particular, we investigate connections hyperquasigroups with binary quasigroups.     

States on <Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript> algebras

The aim of this paper is to introduce the notion of states on R ₀ algebras and investigate some of their properties. We prove that every R ₀ algebra possesses at least one state. Moreover, we investigate states on weak R ₀ algebras and give some examples to show that, in contrast to R ₀ algebras, there exist weak R ₀ algebras which have no states. We also derive the condition under which finite linearly ordered weak R ₀ algebras have a state. This work is supported by NSFC (No.60605017).     

<Emphasis Type="BoldItalic">H</Emphasis><Subscript>2</Subscript>-Control and the Separation Principle for Discrete-Time Markovian Jump Linear Systems

In this paper we consider the H₂-control problem of discrete-time Markovian jump linear systems. We assume that only an output and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed-loop system is mean square stable and minimizes the H₂-norm of the system. As in the case with no jumps, we show that an optimal controller can be obtained from two sets of coupled algebraic Riccati equations, one associated with the optimal control problem when the state variable is available, and the other associated with the optimal filtering problem. This is the principle of separation for discrete-time Markovian jump linear systems. When there is only one mode of operation our results coincide with the traditional separation principle for the H₂-control of discrete-time linear systems. Date received: June 1, 2001. Date revised: October 13, 2003.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> DOF control for uncertain T-S fuzzy neutral systems

This paper investigates the problem of robust H _∞ dynamic output-feedback (DOF) control for a class of uncertain T-S fuzzy neutral systems with linear fractional parametric uncertainties. The aim is to design a full-order fuzzy DOF controller that ensures asymptotic stability of the closed-loop system and guarantees a prescribed H ^∞ performance level on disturbance attenuation for all admissible uncertainties. Based on the Lyapunov-Krasoviskii functional and the Barbalat lemma, delay-dependent sufficient conditions for the solvability of this problem are presented in terms of LMIs. Finally, a simulation example is provided to demonstrate the effectiveness and applicability of the proposed method.     

(Weak) Dual hyper <Emphasis Type="Italic">K</Emphasis>-ideals

In this note by considering the notion of (weak) dual hyper K-ideal, we obtain some related results. After that we determine the relationships between (weak) dual hyper K-ideals and (weak) hyper K-ideals. Finally, we give a characterization of hyper K-algebras of order 3 or 4 based on the (weak) dual hyper K-ideals.     

An HLLC Scheme to Solve The <Emphasis Type="Italic">M</Emphasis><Subscript>1</Subscript> Model of Radiative Transfer in Two Space Dimensions

The M ₁ radiative transfer model is considered in the present work in order to simulate the radiative fields and their interactions with the matter. The model is governed by an hyperbolic system of conservation laws supplemented by relaxation source terms. Several difficulties arise when approximating the solutions of the model; namely the positiveness of the energy, the flux limitation and and the limit diffusion behavior have to be satisfied. An HLLC scheme is exhibited and it is shown to satisfy all the required properties. A particular attention is payed concerning the approximate extreme waves. These approximations are crucial to obtain an accurate scheme. The extension to the full 2D problem is proposed. It satisfies, once again, all the expected properties. Numerical experiments are proposed. They show that the considered scheme is actually less diffusive than the currently used numerical methods.      

Generalized fuzzy filters of <Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript>-algebras

In this paper, we introduce the notions of interval valued -fuzzy filters and interval valued -fuzzy Boolean (implicative) filters in R ₀-algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that an interval valued fuzzy set F in R ₀-algebras is an interval valued -fuzzy Boolean filter if and only if it is an interval valued -fuzzy implicative filter.     

Approximations in <Emphasis Type="Italic">n</Emphasis>-ary algebraic systems

Algebraic systems have many applications in the theory of sequential machines, formal languages, computer arithmetics, design of fast adders and error-correcting codes. The theory of rough sets has emerged as another major mathematical approach for managing uncertainty that arises from inexact, noisy, or incomplete information. This paper is devoted to the discussion of the relationship between algebraic systems, rough sets and fuzzy rough set models. We shall restrict ourselves to algebraic systems with one n-ary operation and we investigate some properties of approximations of n-ary semigroups. We introduce the notion of rough system in an n-ary semigroup. Fuzzy sets, a generalization of classical sets, are considered as mathematical tools to model the vagueness present in rough systems.     

An Augmented Lagrangian Method for <Emphasis Type="Italic">TV</Emphasis><Subscript><Emphasis Type="Italic">g</Emphasis></Subscript>+<Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-norm Minimization

In this paper, the minimization of a weighted total variation regularization term (denoted TV _g ) with L ¹ norm as the data fidelity term is addressed using the Uzawa block relaxation method. The unconstrained minimization problem is transformed into a saddle-point problem by introducing a suitable auxiliary unknown. Applying a Uzawa block relaxation method to the corresponding augmented Lagrangian functional, we obtain a new numerical algorithm in which the main unknown is computed using Chambolle projection algorithm. The auxiliary unknown is computed explicitly. Numerical experiments show the availability of our algorithm for salt and pepper noise removal or shape retrieval and also its robustness against the choice of the penalty parameter. This last property is useful to attain the convergence in a reduced number of iterations leading to efficient numerical schemes. The specific role of the function g in TV _g is also investigated and we highlight the fact that an appropriate choice leads to a significant improvement of the denoising results. Using this property, we propose a whole algorithm for salt and pepper noise removal (denoted UBR-EDGE) that is able to handle high noise levels at a low computational cost. Shape retrieval and geometric filtering are also investigated by taking into account the geometric properties of the model.     

Classification of optimal (<Emphasis Type="Italic">v</Emphasis>, 4, 1) binary cyclically permutable constant-weight codes and cyclic 2-(<Emphasis Type="Italic">v</Emphasis>, 4, 1) designs with <Emphasis Type="Italic">v</Emphasis> ≤ 76

We classify up to isomorphism optimal (v, 4, 1) binary cyclically permutable constantweight (CPCW) codes with v ≤ 76 and cyclic 2-(73, 4, 1) and 2-(76, 4, 1) designs. There is a one-to-one correspondence between optimal (v, 4, 1) CPCW codes, optimal cyclic binary constant-weight codes with weight 4 and minimum distance 6, (v, 4; ⌎(v − 1)/12⌏) difference packings, and optimal (v, 4, 1) optical orthogonal codes. Therefore, the classification of CPCW codes holds for them too. Perfect (v, 4, 1) CPCWcodes are equivalent to (v, 4, 1) cyclic difference families, and thus (73, 4, 1) cyclic difference families are classified too.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> fuzzy control for discrete-time nonlinear systems

This paper studies the problem of robust H _∞ control for discrete-time nonlinear systems presented as Takagi—Sugeno’s fuzzy models. The generalized non-parallel distributed compensation (non-PDC) law and non-quadratic Lyapunov function is constructed by the proposed homogeneouspolynomially basis-dependent matrix function (HPB-MF for abbreviation). Based on the generalized non-PDC law and non-quadratic Lyapunov function, some linear matrix inequalities (LMIs) are obtained by exploiting the possible combinations of the basis functions. These LMIs ensure the asymptotic stability of the closed-loop system and guarantee a norm bound constraint on disturbance attenuation. In addition, it is shown that the LMIs become less conservative as the degree of HPB-MF increases. The merit of the methods presented in this paper lies in their less conservatism than other methods, as shown by a numerical example borrowed from the literature.     

A fast and adaptive method for complex-valued SAR image denoising based on <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript> norm regularization

This paper developed a fast and adaptive method for SAR complex image denoising based on l _k norm regularization, as viewed from parameters estimation. We firstly establish the relationship between denoising model and ill-posed inverse problem via convex half-quadratic regularization, and compare the difference between the estimator variance obtained from the iterative formula and biased Cramer-Rao bound, which proves the theoretic flaw of the existent methods of parameter selection. Then, the analytic expression of the model solution as the function with respect to the regularization parameter is obtained. On this basis, we study the method for selecting the regularization parameter through minimizing mean-square error of estimators and obtain the final analytic expression, which resulted in the direct calculation, high processing speed, and adaptability. Finally, the effect of regularization parameter selection on the resolution of point targets is analyzed. The experiment results of simulation and real complex-valued SAR images illustrate the validity of the proposed method. Supported by the National Natural Science Foundation of China (Grant No. 60572136), the Fundamental Research Fund of NUDT (Grant No. JC0702005)     

Pre-compensator selection for <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> loop shaping control

In this paper, an attempt has been made to address on the design of pre-compensator to obtain the solution of H _∞ loop-shaping control problem. Two different design techniques have been proposed where the first one is based on singular value decomposition (SVD) technique along with the matrix perturbation approach; the other one is focused in linear matrix inequality (LMI) framework leading to minimize the condition number of the pre-compensator that, in turn, reduces loop deterioration. A numerical example has been considered to illustrate the effectiveness of the proposed method.     

Electrical properties and crystallization behavior of Sb<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se<Subscript>100−<Emphasis Type="Italic">x</Emphasis></Subscript> thin films

The structural transformation and transformation kinetics of Sb _x Se_100−x films (60 ≤ x ≤ 70) were studied to investigate the feasibility of applying Sb _x Se_100−x alloys in phase-change nonvolatile memories. The temperature-dependent van der Pauw measurements, Hall measurements, X-ray diffraction and a static tester were used to investigate the electrical properties and crystallization behavior of the Sb _x Se_100−x films. The sheet resistance difference between amorphous and crystalline state was higher than 10⁴ Ω per square According to Hall measurement, Sb _x Se_100−x films have p-type conduction and the Hall mobility and carrier concentration increases with the increase in Sb content. The crystalline structure of the metastable phase of Sb _x Se_100−x alloys, which plays a major roll in fast crystallization, is similar to that of Sb₂Te (rhombohedral structure). The transition temperature, sheet resistance and activation energy for transformation decrease as the amount of Sb increases in the Sb _x Se_100−x film. Applying the Kissinger method, the activation energies for crystallization were in the range from 1.90 ± 0.15 to 4.16 ± 0.28 eV. The desired crystallization speed can be obtained by a systematic change of the composition owing to the variation of the activation barrier with stoichiometry.     

Parallel bisecting <Emphasis Type="Italic">k</Emphasis>-means with prediction clustering algorithm

In this paper, we propose a new parallel clustering algorithm, named Parallel Bisecting k-means with Prediction (PBKP), for message-passing multiprocessor systems. Bisecting k-means tends to produce clusters of similar sizes, and according to our experiments, it produces clusters with smaller entropy (i.e., purer clusters) than k-means does. Our PBKP algorithm fully exploits the data-parallelism of the bisecting k-means algorithm, and adopts a prediction step to balance the workloads of multiple processors to achieve a high speedup. We implemented PBKP on a cluster of Linux workstations and analyzed its performance. Our experimental results show that the speedup of PBKP is linear with the number of processors and the number of data points. Moreover, PBKP scales up better than the parallel k-means with respect to the dimension and the desired number of clusters. This research was supported in part by AFRL/Wright Brothers Institute (WBI).     

Maximum <Emphasis Type="Italic">k</Emphasis>-Splittable <Emphasis Type="Italic">s</Emphasis>,<Emphasis Type="Italic">t</Emphasis>-Flows

Given a graph with a source and a sink node, the NP-hard maximum k-splittable s,t-flow (M k SF) problem is to find a flow of maximum value from s to t with a flow decomposition using at most k paths. The multicommodity variant of this problem is a natural generalization of disjoint paths and unsplittable flow problems. Constructing a k-splittable flow requires two interdepending decisions. One has to decide on k paths (routing) and on the flow values for the paths (packing). We give efficient algorithms for computing exact and approximate solutions by decoupling the two decisions into a first packing step and a second routing step. Usually the routing is considered before the packing. Our main contributions are as follows: (i) We show that for constant k a polynomial number of packing alternatives containing at least one packing used by an optimal M k SF solution can be constructed in polynomial time. If k is part of the input, we obtain a slightly weaker result. In this case we can guarantee that, for any fixed ε>0, the computed set of alternatives contains a packing used by a (1−ε)-approximate solution. The latter result is based on the observation that (1−ε)-approximate flows only require constantly many different flow values. We believe that this observation is of interest in its own right. (ii) Based on (i), we prove that, for constant k, the M k SF problem can be solved in polynomial time on graphs of bounded treewidth. If k is part of the input, this problem is still NP-hard and we present a polynomial time approximation scheme for it.     

Particle swarm optimization-based fixed-structure <Emphasis Type="Italic">ℋ</Emphasis><Subscript>∞</Subscript> control design

In this paper, a new robust fixed-structure ℋ _∞ controller design based on the Particle Swarm Optimization (PSO) technique is proposed. The optimization-based structured synthesis problem is formulated and solved by a constrained PSO algorithm. In the proposed approach, the ℋ _∞ controller’s structure is selectable. PI and PID controller structures are especially adopted. The case study of an electrical DC drive benchmark is adopted to illustrate the efficiency and viability of the proposed control approach. A comparison to another similar evolutionary algorithm, such as Genetic Algorithm Optimization (GAO), shows the superiority of the PSO-based method to solve the formulated optimization problem. Simulations and experimental results show the advantages of simple structure, lower order and robustness of the proposed controller.     

<Emphasis Type="Italic">k</Emphasis>-Nearest-Neighbor Clustering and Percolation Theory

Let P be a realization of a homogeneous Poisson point process in ℝ ^d with density 1. We prove that there exists a constant k _d , 1<k _d <∞, such that the k-nearest neighborhood graph of P has an infinite connected component with probability 1 when k≥k _d . In particular, we prove that k ₂≤213. Our analysis establishes and exploits a close connection between the k-nearest neighborhood graphs of a Poisson point set and classical percolation theory. We give simulation results which suggest k ₂=3. We also obtain similar results for finite random point sets. Part of the work was done while S.-H. Teng was at Xerox Palo Alto Research Center and MIT. The work of F.F. Yao was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 1165/04E].