Coordinated Collective Motion of Groups of Autonomous Mobile Robots with Directed Interconnected Topology

Coordinated collective motion of groups of autonomous mobile robots is studied. A qualitative analysis for the collective dynamics of multiple autonomous robots with directed interconnected topology using nearest neighbor rules is given. A necessary and sufficient graphical condition is proposed to guarantee that the headings of all robots converge to the same heading. The graph having a globally reachable node plays a crucial role in convergence analysis. Furthermore, we show that the globally reachable node having no neighbors serves as a group leader as a special case Supported in part by National Natural Science Foundation of China under the grant 60604001 and 60674081, Natural Science Research Project of Hubei Provincial Department of Education under the grant D20081306 and Scientific Innovation Team Project of Hubei Provincial College under the grant T200809.     

Delay-dependent robust H ∞ control for uncertain fuzzy Markovian jump systems

This paper is concerned with the problem of delay-dependent robust H _∞ control for uncertain fuzzy Markovian jump systems with time delays. The purpose is to design a mode-dependent state-feedback fuzzy controller such that the closed-loop system is robustly stochastically stable and satisfies an H _∞ performance level. By introducing slack matrix variables, a delay-dependent sufficient condition for the solvability of the problem is proposed in terms of linear matrix inequalities. An illustrative example is finally given to show the applicability and effectiveness of the proposed method. Recommended by Editorial Board member Young Soo Suh under the direction of Editor Jae Weon Choi. This work is supported by the National Science Foundation for Distinguished Young Scholars of P. R. China under Grant 60625303, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20060288021, and the Natural Science Foundation of Jiangsu Province under Grant BK2008047. Yashun Zhang received the B.S. and M.S. degrees in Control Science and Control Engineering from Hefei University of Science and Technology in 2003 and 2006. He is currently a Ph.D. student in Control Science and Control Engineering, Nanjing University of Science and Technology. His research interests include fuzzy control, sliding mode control and nonlinear control. Shengyuan Xu received the Ph.D. degree in Control Science and Control Engineering from Nanjing University of Science and Technology in 1999. His research interests include robust filtering and control, singular systems, time-delay systems and nonlinear systems. Jihui Zhang is a Professor in the School of Automation Engineering of Qingdao University, China. His main areas of interest are discrete event dynamic systems, production planning and control, and operations research.     

A note on the perturbation of an outer inverse

In this note, we present an explicit formula for perturbations of an outer inverse under certain conditions, which extends previous results. The second author was supported by the National Natural Science Foundation of China under grant 10871051 and the Shanghai Education Committee under grant 08511501703.     

Minimum-energy wavelet frame on the interval

The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper. They are as follows： 1） give the definition of interval minimum-energy wavelet frame; 2） give the necessary and sufficient conditions for the minimum-energy frames for L^2[0,1]; 3） present the construction algorithm for minimum-energy wavelet frame associated with refinable functions on the interval with any support y; 4） give the decomposition and reconstruction formulas of the minimum-energy frame on the interval [0,1],     

A proof technique for communicating sequential processes

Summary Proof rules are presented for an extension of Hoare's Communicating Sequential Processes. The rules deal with total correctness; all programs terminate in the absence of deadlock. The commands send and receive are treated symmetrically, simplifying the rules and allowing send to appear in guards. Also given are sufficient conditions for showing that a program is deadlock-free. An extended example illustrates the use of the technique.This research was supported in part by the National Science Foundation under grant MCS-7622360.     

Local tests for consistency of support hyperplane data

Support functions and samples of convex bodies in R ⁿ are studied with regard to conditions for their validity or consistency. Necessary and sufficient conditions for a function to be a support function are reviewed in a general setting. An apparently little known classical such result for the planar case due to Rademacher and based on a determinantal inequality is presented and a generalization to arbitrary dimensions is developed. These conditions are global in the sense that they involve values of the support function at widely separated points. The corresponding discrete problem of determining the validity of a set of samples of a support function is treated. Conditions similar to the continuous inequality results are given for the consistency of a set of discrete support observations. These conditions are in terms of a series of local inequality tests involving only neighboring support samples. Our results serve to generalize existing planar conditions to arbitrary dimensions by providing a generalization of the notion of nearest neighbor for plane vectors which utilizes a simple positive cone condition on the respective support sample normals.This work partially supported by the Center for Intelligent Control Systems under the U.S. Army Research Office Grant DAAL03-92-G-0115, the Office of Naval Research under Grant N00014-91-J-1004, and the National Science Foundation under Grant MIP-9015281.Partially supported by the National Science Foundation under grant IRI-9209577 and by the U.S. Army Research Office under grant DAAL03-92-G-0320     

Ways to sparse representation: An overview

Many algorithms have been proposed to find sparse representations over redundant dictionaries or transforms. This paper gives an overview of these algorithms by classifying them into three categories: greedy pursuit algorithms, l _p norm regularization based algorithms, and iterative shrinkage algorithms. We summarize their pros and cons as well as their connections. Based on recent evidence, we conclude that the algorithms of the three categories share the same root: l _p norm regularized inverse problem. Finally, several topics that deserve further investigation are also discussed. Supported by the Joint Research Fund for Overseas Chinese Young Scholars of the National Natural Science Foundation of China (Grant No. 60528004) and the Key Project of the National Natural Science Foundation of China (Grant No. 60528004)     

Reduction Algorithms Based on Discernibility Matrix：The Ordered Atributes Method

In this Paper,we present reduction algorithms based on the principle of Skowron‘s discernibility matrix-the ordered attributes method.The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved.Since a discernibility matrix requires the size of the memory of |U|^2,U is a universe of bojects,it would be impossible to apply these algorithms directly to a massive object set.In order to solve the problem,a so=called quasi-discernibility matrix and two reduction algorithms are prpopsed.Although the proposed algorithms are incomplete for Pawlak reduct,their optimal paradigms ensure the completeness as long as they satisfy some conditions.Finally,we consider the problem on the reduction of distributive object sets.     

Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation

This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics, respectively. Secondly, it puts forward and discusses the definitions and theories of fractional stationary point, fractional equilibrium coefficient, fractional stable coefficient, and fractional grayscale co-occurrence matrix. At the same time, it particularly discusses frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively. Furthermore, it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly, based on the above-mentioned discus- sion, it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images.     

Stability analysis for recurrent neural networks with time-varying delay

This paper is concerned with the stability analysis for static recurrent neural networks （RNNs） with time-varying delay. By Lyapunov functional method and linear matrix inequality technique, some new delay-dependent conditions are established to ensure the asymptotic stability of the neural network. Expressed in linear matrix inequalities （LMIs）, the proposed delay-dependent stability conditions can be checked using the recently developed algorithms. A numerical example is given to show that the obtained conditions can provide less conservative results than some existing ones.     

The Impact of Non-Gaussian Distribution Traffic on Network Performance

Recent extensive measurements of real-life traffic demonstrate that the probability density function of the traffic in non-Gaussian.If a traffic model does not capture this characteristics,any analytical or simulation results will not be accurate.In this work,we study the impact of non-Gaussian traffic on network performance,and present an approach that can accurately model the marginal distribution of real-life traffic.Both the long-and short-range autocorrelations are also accounted.We show that the removal of non-Gaussian components of the process does not change its correlation structure,and we validate our promising procedure by simulations.     

Structure of aura and co-occurrence matrices for the Gibbs texture model

The aura matrix of an image indicates how much of each gray level is present in the neighborhood of each other gray level and generalizes the popular texture-analysis tool, the co-occurrence matrix. In this paper we show that interesting structure appears in both the aura and co-occurrence matrices for textures that are synthesized from Gibbs random-field models. We derive this structure by characterizing configurations of the distribution that are most likely to be synthesized when the Gibbs energy is minimized. This minimization is an important part of applications that use the Gibbs model within a Bayesian estimation framework for maximum a posteriori (MAP) estimation. In particular, we show that the aura matrix will become tridiagonal for an attractive autobinomial field when suitable constraints exist on the histogram, neighborhood, and image sizes. Under the same constraints, but where the field is repulsive instead of attractive, the matrix will become antitridiagonal. The interpretation of this structure is especially significant for modeling textures with minimum-energy configurations: zeros in the matrix prohibit certain colors from occurring next to each other, thus prohibiting large classes of textures from being formed.This work was supported by the National Science Foundation and the Defense Advanced Research Projects Agency under grant MIP-88-14612, the National Science Foundation under grant IRI-8719920, and the Rome Air Development Center of the U.S. Air Force Systems Command and the Defense Advanced Research Projects Agency under contract F30602-89-C-0022.     

On Local Stratifiability of Logic Prograns and Databases

In this paper,we deal with the problem of verifying local stratifiability of logic programs and databases presented by Przymusinski.Necessary and sufficient condition for the local stratifiability of logic programs are presented and algorithms of performing the verification are developed.Finally,we prove that a database D B containing clauses with disjunctive consequents can be easily converted into a logic program P such that D B is locally statified iff P is locally stratified.     

Globally exponentially attractive sets of the family of Lorenz systems

In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b→ 1^＋ and a→0^＋, for which the previous methods failed, have been solved using a unified formula.     

Dynamic file grouping for load balancing in streaming media clustered server systems

A dynamic file grouping strategy is presented to address the load balancing problem in streaming media clustered server systems. This strategy increases the server cluster availability by balancing the workloads among the servers within a cluster. Additionally, it improves the access hit ratio of cached files in delivery servers to alleviate the limitation of I/O bandwidth of storage node. First, the load balancing problem is formulated as a two layers semi-Markov switching state-space control process. This analytic model captures the behaviors of streaming media clustered server systems accurately, and is with constructional flexibility and scalability. Then, a policy iteration based reinforcement learning algorithm is proposed to optimize the file grouping policy online. By utilizing the features of the event-driven policy, the proposed optimization algorithm is adaptive and with less computational cost. Simulation results demonstrate the effectiveness of the proposed approach. Recommended by Editor Hyun Seok Yang. This work was supported by the National Natural Science Foundation of China under grant Nos. 60774038, 60574065, National 863 HI-TECH Research & Development Plan of China under grant Nos. 2006AA01Z114, 2008AA01A317, Natural Science Foundation of Anhui Province under grant No. 070412063, Graduate Student Innovation Foundation of USTC under grant No. KD2006036, and Science Research Development Foundation of HFUT under grant No. GDBJ2008-045. Qi Jiang received the B.S. degree in Industrial Electrical Automation from Southeast University in 1989 and the Ph.D. degree in Control Science and Engineering from University of Science and Technology of China in 2008. He is currently a Post-doc in USTC. His research interests include optimization and control of stochastic dynamic systems, and performance analysis and optimization of network communication systems. Hong-Sheng Xi received the M.S. degree in Applied Mathematics from University of Science and Technology of China in 1977. He is currently a Professor in Department of Automation, USTC. His research interests include discrete event dynamic systems, performance analysis and optimization of network communication systems, robust control, and network security. Bao-Qun Yin received the B.S. degree in Mathematics from Sichuan University in 1985, the M.S. degree in Applied Mathematics and the Ph.D. degree in Pattern Recognition and Intelligent Systems from University of Science and Technology of China in 1993 and 1998, respectively. He is currently a Professor in Department of Automation, USTC. His research interests include discrete event dynamic systems, and Markov decision processes.     

A note on overshoot estimation in pole placements

In this note we show that for a given controllable pair (A, B) and any λ>0, a gain matrix K can be chosen so that the transition matrix e~((A+BK)t) of the system =(A+BK)x decays at the exponential rate e~(-λt) and the overshoot of the transition matrix can be bounded by Mλ~L for some constants M and L that are independent of λ. As a consequence, for any h>0, a gain matrix K can be chosen so that the magnitude of the transition matrix e~((A+BK)t) can be reduced by1/2 (or by any given portion) over [0, h]. An interesting application of the result is in the stabilization of switched linear systems with any given switching rate (see [1]).     

Convergence of bpsd method for T (q,r) matrix

In this paper, we obtain a necessary and sufficient condition, when the coefficient matrix A of the equation Ax = f considered is a T(l, 1) matrix, a sufficient condition, when A is a T(l, 2) or T(2, 1) matrix for the convergence of BPSD method. We also obtain the optimum parameters and the optimum rate of convergence of BPSD method, when A is T(l, 1) matrix and a necessary and sufficient condition, when A is positive definite and we point out that the necessary and sufficient condition in [1] and [9] is only sufficient.     

Strong decoupling in singular systems

This paper considers the dynamic decoupling problem under state feedback control in singular systems. Control laws are suggested for a notion of strong decoupling which is characterized by the physical realizability of control laws and the lack of impulsive modes in closed-loop systems.This project was supported by the National Natural Science Foundation of China.     

Second Attribute Algorithm Based on Tree Expression

One view of finding a personalized solution of reduct in an information system is grounded on the viewpoint that attribute order can serve as a kind of semantic representation of user requirements. Thus the problem of finding personalized solutions can be transformed into computing the reduct on an attribute order. The second attribute theorem describes the relationship between the set of attribute orders and the set of reducts, and can be used to transform the problem of searching solutions to meet user requirements into the problem of modifying reduct based on a given attribute order. An algorithm is implied based on the second attribute theorem, with computation on the discernibility matrix. Its time complexity is O（n^2 × m） （n is the number of the objects and m the number of the attributes of an information system）. This paper presents another effective second attribute algorithm for facilitating the use of the second attribute theorem, with computation on the tree expression of an information system. The time complexity of the new algorithm is linear in n. This algorithm is proved to be equivalent to the algorithm on the discernibility matrix.