Robust fuzzy stabilization of dithered chaotic systems using island-based random optimization algorithm

Applying dither to highly nonlinear systems may suppress chaotic phenomena, but dynamic performance, such as convergence rate and disturbance attenuation, is usually not guaranteed. This paper presents a dithered H_∞ robust fuzzy control scheme to stabilize chaotic systems that ensures disturbance attenuation bounds. In the proposed scheme, Takagi-Sugeno (T-S) fuzzy linear models are used to describe the relaxed models of the dithered chaotic system, and fuzzy controllers are designed based on an extension to the concept of parallel distributed compensation (PDC). Sufficient condition for the existence of the H_∞ robust fuzzy controllers is presented in terms of a novel linear matrix inequalities (LMI) form which takes full consideration of modeling error and disturbances, but cannot be solved by the standard procedures. In order to solve the LMI problem and to identify the chaotic systems as T-S fuzzy modes, we propose a compound optimization strategy called the island-based random-walk algorithm (IRA). The algorithm is composed of a set of communicating random-walk optimization procedures concatenated with the down-hill simplex method. The design procedure and validity of the proposed scheme is demonstrated via numerical simulation of the dithered fuzzy control of a chaotic system.     

Software testing processes as a linear dynamic system

Software testing is essential for software reliability improvement and assurance, and the processes of software testing are intrinsically dynamic. However they are seldom investigated in a mathematically rigorous manner. In this paper a theoretical study is presented to examine the dynamic behavior of software testing. More specifically, a set of simplifying assumptions is adopted to formulate and quantify the software testing processes. The mathematical formulae for the expected number of observed software failures are rigorously derived, the bounds and trends of the expected number of observed software failures are analyzed, and the variance of the number of observed software failures is examined. On the other hand, it is demonstrated that under the simplifying assumptions, the software testing processes can be treated as a linear dynamic system. This suggests that the software testing processes could be classified as linear or non-linear, and there be intrinsic link between software testing and system dynamics.     

1D correlation filter based class-dependence feature analysis for face recognition

In this paper, a novel one-dimensional correlation filter based class-dependence feature analysis (1D-CFA) method is presented for robust face recognition. Compared with original CFA that works in the two dimensional (2D) image space, 1D-CFA encodes the image data as vectors. In 1D-CFA, a new correlation filter called optimal extra-class origin output tradeoff filter (OEOTF), which is designed in the low-dimensional principal component analysis (PCA) subspace, is proposed for effective feature extraction. Experimental results on benchmark face databases, such as FERET, AR, and FRGC, show that OEOTF based 1D-CFA consistently outperforms other state-of-the-art face recognition methods. This demonstrates the effectiveness and robustness of the novel method.     

CPU demand for web serving: Measurement analysis and dynamic estimation

Managing the resources in a large Web serving system requires knowledge of the resource needs for service requests of various types. In order to investigate the properties of Web traffic and its demand, we collected measurements of throughput and CPU utilization and performed some data analyses. First, we present our findings in relation to the time-varying nature of the traffic, the skewness of traffic intensity among the various types of requests, the correlation among traffic streams, and other system-related phenomena. Then, given such nature of web traffic, we devise and implement an on-line method for the dynamic estimation of CPU demand.

Assessing resource needs is commonly performed using techniques such as off-line profiling, application instrumentation, and kernel-based instrumentation. Little attention has been given to the dynamic estimation of dynamic resource needs, relying only on external and high-level measurements such as overall resource utilization and request rates. We consider the problem of dynamically estimating dynamic CPU demands of multiple kinds of requests using CPU utilization and throughput measurements. We formulate the problem as a multivariate linear regression problem and obtain its basic solution. However, as our measurement data analysis indicates, one is faced with issues such as insignificant flows, collinear flows, space and temporal variations, and background noise. In order to deal with such issues, we present several mechanisms such as data aging, flow rejection, flow combining, noise reduction, and smoothing. We implemented these techniques in a Work Profiler component that we delivered as part of a broader system management product. We present experimental results from using this component in scenarios inspired by real-world usage of that product.     

A new vertex result for robustness problems with interval matrix uncertainty

This paper¹ addresses a family of robustness problems in which the system under consideration is affected by interval matrix uncertainty. The main contribution of the paper is a new vertex result that drastically reduces the number of extreme realizations required to check robust feasibility. This vertex result allows one to solve, in a deterministic way and without introducing conservatism, the corresponding robustness problem for small and medium size problems. For example, consider quadratic stability of an autonomous n_x dimensional system. In this case, instead of checking vertices, we show that it suffices to check 2^2n_x specially constructed systems. This solution is still exponential, but this is not surprising because the problem is NP-hard. Finally, vertex extensions to multiaffine interval families and some sufficient conditions (in LMI form) for robust feasibility are presented. Some illustrative examples are also given.     

An LMI approach to synthesis subject to almost asymptotic regulation constraints

A multi-objective controller synthesis problem is considered in which an output is to be regulated approximately by assuring a bound on the steady-state peak amplification in response to an infinite-energy disturbance, while also guaranteeing a desired level of performance measured in terms of the worst-case energy gain from a finite-energy input to a performance output. Relying on a characterization of the controllers with which almost asymptotic regulation is accomplished, the problem of guaranteeing the desired level of performance is reduced to solving a system of linear matrix inequalities subject to a set of linear equality constraints. Based on the solution of this system, a procedure is outlined for the construction of a suitable controller whose order is equal to the order of the plant plus the order of the exogenous system.     

Controllability of second-order infinite-dimensional systems

In the paper, the approximate controllability of linear abstract second-order infinite-dimensional dynamical systems is considered. It is proved using the frequency-domain method, that approximate controllability of second-order system can be verified by the approximate controllability conditions for the corresponding simplified first-order system. General results are then applied for approximate controllability investigation of a vibratory dynamical system modeling flexible mechanical structure. Some special cases are also considered. Moreover, remarks and comments on the relationships between different concepts of controllability are given. The paper extends earlier results on approximate controllability of second-order abstract dynamical systems.     

An extension of likelihood-ratio-test for testing linear hypotheses in the baseline-category logit model

A new family of test statistics for testing linear hypotheses in baseline-category logit models is introduced and its asymptotic distribution is obtained. The new family is a natural extension of the classical likelihood ratio test. A simulation study is carried out to find new test statistics that offer an attractive alternative to the classical likelihood ratio test in terms of both exact size and exact power.     

Path Hitting in Acyclic Graphs

An instance of the path hitting problem consists of two families of paths, and ℋ, in a common undirected graph, where each path in ℋ is associated with a non-negative cost. We refer to and ℋ as the sets of demand and hitting paths, respectively. When p∈ℋ and share at least one mutual edge, we say that p hits q. The objective is to find a minimum cost subset of ℋ whose members collectively hit those of . In this paper we provide constant factor approximation algorithms for path hitting, confined to instances in which the underlying graph is a tree, a spider, or a star. Although such restricted settings may appear to be very simple, we demonstrate that they still capture some of the most basic covering problems in graphs. Our approach combines several novel ideas: We extend the algorithm of Garg, Vazirani and Yannakakis (Algorithmica, 18:3–20, 1997) for approximate multicuts and multicommodity flows in trees to prove new integrality properties; we present a reduction that involves multiple calls to this extended algorithm; and we introduce a polynomial-time solvable variant of the edge cover problem, which may be of independent interest. An extended abstract of this paper appeared in Proceedings of the 14th Annual European Symposium on Algorithms, 2006. This work is part of D. Segev’s Ph.D. thesis prepared at Tel-Aviv University under the supervision of Prof. Refael Hassin.     

Numerical simulation of a nonlinearly coupled Schrödinger system: A linearly uncoupled finite difference scheme

This article describes a finite difference scheme which is linearly uncoupled in computation for a nonlinearly coupled Schrödinger system. This numerical scheme is proved to preserve the original conservative properties. Using the discrete energy analysis method, we also prove that the scheme is unconditionally stable and second-order convergent in discrete _L2$L_2$-norm based on some preliminary estimations. The results show that the new scheme is efficiency.