Optimal Control Using Feedback Linearization for a Generalized T-S Model

In this paper, a fuzzy feedback linearization is used to control nonlinear systems described by Takagi-Suengo (T-S) fuzzy systems. In this work, an optimal controller is designed using the linear quadratic regulator (LQR). The well known weighting parameters approach is applied to optimize local and global approximation and modelling capability of T-S fuzzy model to improve the choice of the performance index and minimize it. The approach used here can be considered as a generalized version of T-S method. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the proposed optimal LQR algorithm.

Direct and Converse Theorems for Generalized Bernstein-Type Operators

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.

Best Approximation and Moduli of Smoothness

2010 Mathematics Subject Classification: 41A25, 41A10.

Generalized KPCA by adaptive rules in feature space

Principal component analysis (PCA) is well recognized in dimensionality reduction, and kernel PCA (KPCA) has also been proposed in statistical data analysis. However, KPCA fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named iterative robust KPCA (IRKPCA). IRKPCA works well in dealing with outliers, and can be carried out in an iterative manner, which makes it suitable to process incremental input data. As in the traditional robust PCA (RPCA), a binary field is employed for characterizing the outlier process, and the optimization problem is formulated as maximizing marginal distribution of a Gibbs distribution. In this paper, this optimization problem is solved by stochastic gradient descent techniques. In IRKPCA, the outlier process is in a high-dimensional feature space, and therefore kernel trick is used. IRKPCA can be regarded as a kernelized version of RPCA and a robust form of kernel Hebbian algorithm. Experimental results on synthetic data demonstrate the effectiveness of IRKPCA. © 2010 Taylor & Francis.

Mixtures of g-priors in Generalized Linear Models

Mixtures of Zellner's g-priors have been studied extensively in linear models and have been shown to have numerous desirable properties for Bayesian variable selection and model averaging. Several extensions of g-priors to Generalized Linear Models (GLMs) have been proposed in the literature; however, the choice of prior distribution of g and resulting properties for inference have received considerably less attention. In this paper, we extend mixtures of g-priors to GLMs by assigning the truncated Compound Confluent Hypergeometric (tCCH) distribution to 1/(1+g) and illustrate how this prior distribution encompasses several special cases of mixtures of g-priors in the literature, such as the Hyper-g, truncated Gamma, Beta-prime, and the Robust prior. Under an integrated Laplace approximation to the likelihood, the posterior distribution of 1/(1+g) is in turn a tCCH distribution, and approximate marginal likelihoods are thus available analytically. We discuss the local geometric properties of the g-prior in GLMs and show that specific choices of the hyper-parameters satisfy the various desiderata for model selection proposed by Bayarri et al, such as asymptotic model selection consistency, information consistency, intrinsic consistency, and measurement invariance. We also illustrate inference using these priors and contrast them to others in the literature via simulation and real examples.

A Generalized Fuzzy Linguistic Model for Predicting Component Concentrations in an Optical Gas Sensing System

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NOx, SO2 etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.

A generalized fuzzy linguistic model for predicting component concentrations in an optical gas sensing system

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NO_x, SO₂ etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.

Genetic diversity and connectivity remain high in Holothuria polii (Delle Chiaje 1823) across a coastal lagoon-open sea environmental gradient

Coastal lagoons represent habitats with widely heterogeneous environmental conditions, particularly as regards salinity and temperature,which fluctuate in both space and time. These characteristics suggest that physical and ecological factors could contribute to the genetic divergence among populations occurring in coastal lagoon and opencoast environments. This study investigates the genetic structure of Holothuria polii at a micro-geographic scale across theMar Menor coastal lagoon and nearbymarine areas, estimating the mitochondrial DNA variation in two gene fragments, cytochrome oxidase I (COI) and 16S rRNA (16S). Dataset of mitochondrial sequences was also used to test the influence of environmental differences between coastal lagoon andmarine waters on population genetic structure. All sampled locations exhibited high levels of haplotype diversity and low values of nucleotide diversity. Both genes showed contrasting signals of genetic differentiation (non-significant differences using COI and slight differences using 16S, which could due to different mutation rates or to differential number of exclusive haplotypes. We detected an excess of recent mutations and exclusive haplotypes, which can be generated as a result of population growth. However, selective processes can be also acting on the gene markers used; highly significant generalized additive models have been obtained considering genetic data from16S gene and independent variables such as temperature and salinity.

Root:Shoot Ratio and Specific Leaf Area Along an Elevational Gradient in the Peruvian Andes

Andean montane forests are one of the most diverse ecosystems on Earth, but are also highly vulnerable to climate change. Therefore, the link between plant distribution and ecosystem productivity is a critical point to investigate in these ecosystems. Are the patterns in productivity observed in montane forest due to species turnover along the elevational gradients? Methodological constraints keep this question unanswered. Also, despite their importance, belowground biomass remains poorly quantified and understood. I measured two plant functional traits in seedlings, root:shoot ratio and specific leaf area, to identify different strategies in growth and biomass allocation across elevations. A tradeoff in specific leaf area with elevation was found in only one species, and no generalized directional change was detected with elevations for root:shoot ratio. Lack of information for the ontogeny of the measured plant traits could confounding the analysis.

Ant community richness and composition across a gradient from Eucalyptus plantations to secondary Atlantic Forest

Secondary forests and exotic tree plantations are expanding across tropical landscapes. However, our current understanding of the value of these human-dominated forest landscapes for invertebrate biodiversity conservation is still very poor. In this paper, we use the leaf-litter ant fauna to assess invertebrate diversity in one commercially managed Eucalyptus plantation (four years old), two abandoned plantations of different regeneration ages (16 and 31 years), and one neighboring secondary Atlantic Forest in Southeastern Brazil. There was a clear gradient in species richness from the secondary forest to the managed Eucalyptus plantation; richness and diversity peaked in secondary forest and in the older regenerating Eucalyptus plantation. Significantly more species were recorded in secondary forest samples than in Eucalyptus plantations, but Eucalyptus plantations had a similar level of richness. Furthermore, a non-metric multidimensional scaling analysis revealed clear differences in species composition between the younger managed Eucalyptus plantation (understory absent) and habitats with sub-developed or developed understory. Eucalyptus plantations were characterized by an assemblage of widespread, generalist species very different from those known to occur in core forest habitats of southeastern Brazil. Our results indicate that while older regenerating Eucalyptus plantations can provide habitat to facilitate the persistence of generalist ant species, it is unlikely to conserve most of the primary forest species, such as specialized predators, Dacetini predators, and nomadic species.

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

We study how the crossover exponent, phi, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value phi = 2 for finite diffusion rates and phi = 1 in the limit of infinite diffusion rate.

Epilithic community development on artificial reefs deployed along a cross-shelf environmental gradient off Paraná state, southern Brazil

Concrete modules were deployed on the bottom of the 11, 18 and 30 meters isobaths along a cross-shelf hydrographic gradient off Paraná State, Southern Brazil, with the purpose of studying the colonization of sessile epilithic macroinvertebrates on artificial surfaces. After one year of submersion a total of 63 species of epilithic organisms were identified, dominated by Ostrea puelchana, Chthamalus bisinuatus, Balanus cf spongicola, Astrangia cf rathbuni, Didemnum spp, poryphers and bryozoans. Diversity index and percent cover at reef stations placed at 11, 18 and 30 meters isobaths were respectively 2.28 and 66.7%, 2.79 and 96.6% and 1.66 and 77.4%. Differences of general community structure among the three assemblages were not clearly related to the general environmental conditions at the bottom layers near the reef stations. Turbidity and larval abundance are discussed as important factors affecting colonization processes. Results indicate that depths between 15-20 meters are more suitable for the implementation of large scale artificial reef systems in the inner shelf off Paraná and, possibly, throughout the inner shelves off southern Brazil with similar hydrographic conditions.

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.