Sampling method for linear system reduction

A new method for obtaining reduced order models for single-input-single-output, continuous-time systems is presented. The proposed algorithm matches the transfer functions of the original and the reduced system at 2M points where M is the order of the reduced model. The location of these points depends on a parameter which can be selected to control the accuracy of the approximation and stability. Numerical examples and comparisons with other methods of model reduction are given.     

Walsh Operational Matrices for Fractional Calculus and Their Application to Distributed Systems

The Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems. A new set of orthogonal functions is derived from Walsh functions. By using the new functions, the generalized Walsh operational matrices corresponding to √s, √(s²+ 1), e^-s and e^-√s etc. are established. Several distributed parameter problems are solved by the new approach.     

Stabilities and Settling Times of Nonlinear and Time-varying Feedback Systems

The bounded-input bounded-output stability, finite time stability and settling time of a single-loop feedback system consisting of a nonlinear time-varying gain followed by a linear time-invariant system are investigated via a nonlinear integral inequality. The gain has the form k₀+k₁(t)+k₂(t)g(bd) where g(bd) is a monotonic increasing function. The system is bounded-input bounded-output stable provided the time-varying gains are L¹(0, t8) functions and is finite time stable for bounded gains. The nonlinear integral inequality, which is used to obtain explicit and useful bounds on the output of the system, is also employed to determine the settling time.     

Some properties of a class of biased regression estimators

For the linear statistical model y = Xb + e, X of full column rank estimates of b of the form (C + X′X)⁺X′y are studied, where C commutes with X′X and Q⁺ is the Moore-Penrose inverse of Q. Such estimators may have smaller mean square error, component by component than does the least squares estimator. It is shown that this class of estimators is equivalent to two apparently different classes considered by other authors. It is also shown that there is no C such that (C + X′X)⁺X′Y = My, in which My has the smallest mean square error, component by component. Two criteria, other than tmse, are suggested for selecting C. Each leads to an estimator independent of the unknown b and σ². Subsequently, comparisons are made between estimators in which the C matrices are functions of a parameter k. Finally, it is shown for the no intercept model that standardizing, using a biased estimate for the transformed parameter vector, and retransforming to the original units yields an estimator with larger tmse than the least squares estimator.     

Scattering of plane waves from an eccentrically coated metallic sphere

In this paper the scattering of plane electromagnetic waves from eccentrically coated metallic spheres is considered. Inhomogeneous, surface, singular integral equations are used to formulate the problem. Their solution is obtained in terms of spherical vector wave functions in conjunction with related addition theorems. Analytical, closed-form results are obtained in the case of small eccentricities kd, where d is the distance between the two centers and k the wave number of the dielectric coating. Thus the scattered field and the various scattering cross-sections of the problem are given by expressions of the form: S(d) = S(0)[1+g’(kd)+g”(kd)²+0(kd)³]. Numerical and graphical results for various values of the parameters are also discussed.     

Simplification and Identification of Discrete Transfer Function via Step-response Matching

A computer-aided method for simplification and identification of linear discrete systems via step-response matching is presented. Golub's algorithm for solving least-squares problem is used to find the optimum coefficients of the reduced model. The advantages of this method are (1) for model reduction, both the time response and frequency response within the bandwidth region of the reduced model are very close to those of the original system; and (2) for system identification, the identified model is very close to the original system. In the illustrative examples considered in this paper the results of the proposed method appear to be better than those of other methods in the current literature.     

A simplified stability test for 1-D discrete systems

This paper shows that the stability tests for 1-D discrete systems using the transformation p=(z+z⁻¹) and properties of Chebyshev polynomials developed previously can be directly obtained from the z-domain continued fraction expansion based on the functions (z+1) and (z⁻¹+1) on an alternate basis. Furthermore, it is shown that the root distribution of a polynomial with real coefficient can be determined by the same algorithm.     

Stability criteria for certain classes of nonlinear difference equations

The general mth order difference equation X(n+m)+a₁X(n+m?1)+…+a_mX(n) = F[n,X(n),…,X(n+m?1)] is considered. The stability properties of its solutions are studied using the discrete form of Liapunov's direct method. A quadratic form is selected as a possible Liapunov function V(n,X) and a scheme is developed for determining appropriate conditions on this function to insure that its total difference ΔV(n,X) is negative semi-definite or negative definite with respect to the difference equation. The approach is applied to the fourth-order difference equation in full detail to illustrate the method for determining the conditions which imply either uniform stability or uniform asymptotic stability and specific results are obtained. Several comments on, and extensions of, the work done by Puri and Drake for the cases m = 2 and m = 3 are presented.The results of the present approach in the homogeneous case where F[n,X(n),…,X(n+m?1)] = 0 are compared with the usual Schur-Cohn criteria and are shown to be at least as good.     

Approximation based on orthogonal and almost orthogonal functions

In this paper, we define a class of almost orthogonal rational functions of Legendre type in a new manner. Relations of these functions with classical exponentional functions orthogonal over interval (0, ∞), as well as classical polynomials orthogonal over (0, 1) are explained. Defining relations of these functions can be used for designing almost orthogonal filters. These filters are generators of orthogonal signals and can be successfully applied in finding the best signal approximation in the sense of the mean square error. The filters orthogonal property enables building of physical (in this case electrical) models of dynamical systems (the sources of signals to be approximated) either with less components for the same model accuracy or higher accuracy for the same number of components than the other known models. New filters represent further improvement of previously designed filters, by the same authors, in the sense of simplicity, higher accuracy, lesser approximation time and even a possibility to approximate signals generated by systems with built-in imperfections. Series of experiments were performed to analyze the dependence of approximation accuracy and the number of filters sections.     

Interval fuzzy robust non-fragile finite frequency control for active suspension of in-wheel motor driven electric vehicles with time delay

This paper proposes a fuzzy non-fragile finite frequency H_∞ control algorithm for the active suspension system (ASS) of the electric vehicles driven by in-wheel motors with an advanced dynamic vibration absorber (DVA). Firstly, an interval type-2 Takagi-Sugeno (T-S) fuzzy model is established to formulate the nonlinear time-delay ASS with the uncertainties of sprung mass, unsprung mass, suspension stiffness, and tire stiffness. Secondly, a differential evolution (DE) algorithm is adopted to optimize the parameters of vehicle suspension and DVA. Thirdly, a non-fragile finite frequency H_∞ control controller is developed under the consideration of controller perturbation and input delay to improve the comprehensive performance of the chassis under the finite frequency external disturbances. Finally, simulation tests are carried out to verify the effectiveness of the proposed controller.     

Transfer function realization of a class of doubly-terminated two-variable lossless networks and their application in linear-phase 2-dimensional digital filter design

A method is presented for the design of a class of two-dimensional (2-D) stable digital filters satisfying prescribed magnitude and constant group delay specifications. The design method generates a 2-D digital transfer function which is a product of two transfer functions H₁(z₁,z₂) and H₂(z₁,z₂), corresponding to a recursive filter and a nonrecursive filter, respectively, Component H₁(z₁,z₂) ensures a wave-digital realization, that is, the design method guarantees the generation of a corresponding analog function H_1A(s₁,s₂) which is realizable as the transfer function of a doubly-terminated two-variable lossless network. Thus the design technique ensures that not only is a given frequency response achieved, but also the generated transfer function is realizable as a cascade of a wave-digital filter and a nonrecursive digital filter. The class of filters considered here is one in which the doubly-terminated analog network used to realize the wave digital filter is a cascade of s₁- and s₂-variable lossess two-ports with all their transmission zeros at infinity.     

Iterative radial basis functions neural networks as metamodels of stochastic simulations of the quality of search engines in the World Wide Web

Stochastic simulation has been very effective in many domains but never applied to the WWW. This study is a premiere in using neural networks in stochastic simulation of the number of rejected Web pages per search query. The evaluation of the quality of search engines should involve not only the resulting set of Web pages but also an estimate of the rejected set of Web pages. The iterative radial basis functions (RBF) neural network developed by Meghabghab and Nasr [Iterative RBF neural networks as meta-models for stochastic simulations, in: Second International Conference on Intelligent Processing and Manufacturing of Materials, IPMM’99, Honolulu, Hawaii, 1999, pp. 729–734] was adapted to the actual evaluation of the number of rejected Web pages on four search engines, i.e., Yahoo, Alta Vista, Google, and Northern Light. Nine input variables were selected for the simulation: (1) precision, (2) overlap, (3) response time, (4) coverage, (5) update frequency, (6) boolean logic, (7) truncation, (8) word and multi-word searching, (9) portion of the Web pages indexed. Typical stochastic simulation meta-modeling uses regression models in response surface methods. RBF becomes a natural target for such an attempt because they use a family of surfaces each of which naturally divides an input space into two regions X+ and X− and the n patterns for testing will be assigned either class X+ or X−. This technique divides the resulting set of responses to a query into accepted and rejected Web pages. To test the hypothesis that the evaluation of any search engine query should involve an estimate of the number of rejected Web pages as part of the evaluation, RBF meta-model was trained on 937 examples from a set of 9000 different simulation runs on the nine different input variables. Results show that two of the variables can be eliminated which include: response time and portion of the Web indexed without affecting evaluation results. Results show that the number of rejected Web pages for a specific set of search queries on these four engines very high. Also a goodness measure of a search engine for a given set of queries can be designed which is a function of the coverage of the search engine and the normalized age of a new document in result set for the query. This study concludes that unless search engine designers address the issue of rejected Web pages, indexing, and crawling, the usage of the Web as a research tool for academic and educational purposes will stay hindered.     

Study on stability and stabilizability of discrete-time mean-field stochastic systems

This paper is to study the mean square stabilizability and regional stability of discrete-time mean-field stochastic systems. Firstly, a necessary and sufficient condition is presented via the spectrum of linear operator to illustrate the stabilizability of discrete-time mean-field stochastic systems. B(0, γ)-stabilizability is introduced and transformed into solving linear matrix inequalities (LMIs). Secondly, B_M-stability is characterized, especially, the stabilities of circular region, sector region and annulus regions are discussed extensively. Finally, as applications, it is shown that B(0, γ₁; γ₂)-stability has close relationship with the decay rate of the system state response and the Lyapunov exponent.     

Analysis of time-varying discrete systems using discrete legendre orthogonal polynomials

A finite series expansion method using discrete Legendre orthogonal polynomials (DLOPs) is applied to analyze linear time-varying discrete systems. An effective algorithm is derived to establish a representation which relates the DLOP coefficient vector of a product function to those of its two-component functions. By using this representation, along with the time-shift operational matrix of DLOP, a linear time-varying difference equation is converted into a set of linear algebraic equations. It is therefore convenient for computer computation.     

Adaptive stabilization of linear and nonlinear plants in the presence of large and arbitrarily fast variations of the parameters

The problem of adaptive stabilization of a class of continuous-time and time-varying nonlinear plants is treated in this paper. The control scheme guarantees that the state of the plant, with bounded time-varying parameters, asymptotically converges to zero. For the nonlinear case with n²+n unknown parameters (n time-varying and n² constant), when the control matrix B is unknown the controller has to adjust n²+1 parameters providing only local stability results. On the contrary, when the control matrix B is known only one parameter has to be adjusted and the proposed scheme provides global stability results. The general methodology is particularized for the linear case with 2n² unknown parameters (n² time-varying and n² constant), adjusting n²+1 parameters when the control matrix B is unknown and guarantees only local stability results, whereas in the case when the control matrix B is known only one parameter has to be adjusted and the proposed scheme provides global stability results.     

Biomineralization of a calcifying ureolytic bacterium Microbacterium sp. GM-1

BackgroundBiomineralization is a significant process performed by living organisms in which minerals are produced through the hardening of biological tissues. Herein, we focus on calcium carbonate precipitation, as part of biomineralization, to be used in applications for environmental protection, material technology, and other fields. A strain GM-1, Microbacterium sp. GM-1, isolated from active sludge, was investigated for its ability to produce urease and induce calcium carbonate precipitation in a metabolic process.ResultsIt was discovered that Microbacterium sp. GM-1 resisted high concentrations of urea up to 60 g/L. In order to optimize the calcification process of Microbacterium sp. GM-1, the concentrations of Ni^2 + and urea, pH value, and culture time were analyzed through orthogonal tests. The favored calcite precipitation culture conditions were as follows: the concentration of Ni^2 + and urea were 50 μM and 60 g/L, respectively, pH of 10, and culture time of 96 h. Using X-ray diffraction analysis, the calcium carbonate polymorphs produced by Microbacterium sp. GM-1 were proven to be mainly calcite.ConclusionsThe results of this research provide evidence that Microbacterium sp. GM-1 can biologically induce calcification and suggest that strain GM-1 may play a potential role in the synthesis of new biominerals and in bioremediation or biorecovery.     

Role of HAMP Genetic Variants on Pathophysiology of Iron Deficiency Anemia

Hepcidin is a 25-amino acid peptide hormone produced by hepatocytes and plays a key role in body iron metabolism. Hepcidin deficiency is the cause of iron overload in hereditary hemochromatosis, iron-loading anemia, and its excess is associated with anemia of inflammation, chronic disease and iron deficiency anemia (IDA). The aims of this study was to evaluate HAMP gene mutation, namely IVS2 + 1(–G) (c.148–150 + 1del) and Gly71 Asp (c.212G > A (rs104894696) association with iron status in IDA conditions. Our study participants were 500 IDA patients and 550 age and sex-matched healthy controls. Hepcidin, ferritin and CRP analysis was done by ELISA method while ESR analysis was done according to Wintrobe method. CBC analysis was done by auto-analyzer. Two mutations in the HAMP genes were analysed by PCR RFLP method. Among the IDA patients, 7 were heterozygous for Met50del IVS2 + 1(–G) mutation. Nine IDA patients were heterozygous for G71D G–A mutation and homozygous were not identified in both mutations.Controls were showing heterozygous frequency 1.8 and 2.1% of Met50del IVS2 + 1(–G) and G71D G–A mutations respectively. Mutation of HAMP (Met50del IVS2 + 1(–G) and G71D G–A) were clinically associated with IDA and act as modulator of disease.     

H2 and H∞ optimal model reduction using genetic algorithms

The mathematical modeling of most physical systems, such as aerospace systems, heat processes, telecommunication systems, transmission lines and chemical reactors, results in complex high order models. The complexity of the models imposes a lot of difficulties in analysis, simulation and control designs. Several analytical model reduction techniques have been proposed in literature over the past few decades to reduce these difficulties. However, most of the optimal techniques follow computationally demanding, time consuming, iterative procedures that usually result in non-robustly stable models with poor frequency response resemblance to the original high order model in some frequency ranges. Genetic Algorithm (GA) has proved to be an excellent optimization tool in the past few years. Therefore, the aim of this paper will be to use GA to solve H₂ and H_∞ norm model reduction problems, and help obtain globally optimized nominal models.