The non-twist standard map with robust tori

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Robust tori in a double-waved Hamiltonian model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Robust tori-like Lagrangian coherent structures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effect of robust torus on the dynamical transport

In the present work, we quantify the fraction of trajectories that reach a specific region of the phase space when we vary a control parameter using two symplectic maps: one non-twist and another one twist. The two maps were studied with and without a robust torus. We compare the obtained patterns and we identify the effect of the robust torus on the dynamical transport. We show that the effect of meandering-like barriers loses importance in blocking the radial transport when the robust torus is present.

Interference of robust tori on the resonance overlap

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Short term hydroelectric scheduling combining network flow and interior point approaches

In this paper, short term hydroelectric scheduling is formulated as a network flow optimization model and solved by interior point methods. The primal-dual and predictor-corrector versions of such interior point methods are developed and the resulting matrix structure is explored. This structure leads to very fast iterations since it avoids computation and factorization of impedance matrices. For each time interval, the linear algebra reduces to the solution of two linear systems, either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored off-line. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved, although its size is reduced to the number of generating units and is not a function of time intervals. These methods were applied to IEEE and Brazilian power systems, and numerical results were obtained using a MATLAB implementation. Both interior point methods proved to be robust and achieved fast convergence for all instances tested. (C) 2004 Elsevier Ltd. All rights reserved.

Well-conditioned robust observer for detection of family systems components

A new concept of fault detection and isolation using robust observation for systems with random noises is presented. The method selects the parameters from components that may fault during the process and constructs well conditioned robust observers, considering sensors faults. To isolate component failures via robust observation, a bank of detection observers is constructed, where each observer is only sensitive to one specified component failure while robust to all other component failures.

An alternative approach to solve convergence problems in the backpropagation algorithm

The multilayer perceptron network has become one of the most used in the solution of a wide variety of problems. The training process is based on the supervised method where the inputs are presented to the neural network and the output is compared with a desired value. However, the algorithm presents convergence problems when the desired output of the network has small slope in the discrete time samples or the output is a quasi-constant value. The proposal of this paper is presenting an alternative approach to solve this convergence problem with a pre-conditioning method of the desired output data set before the training process and a post-conditioning when the generalization results are obtained. Simulations results are presented in order to validate the proposed approach.

Robust state-derivative feedback LMI-based designs for multivariable linear systems

In some practical problems, for instance in the control systems for the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. New necessary and sufficient linear matrix inequalities (LMI) conditions for the design of state-derivative feedback for multi-input (MI) linear systems are proposed. For multi-input/multi-output (MIMO) linear time-invariant or time-varying plants, with or without uncertainties in their parameters, the proposed methods can include in the LMI-based control designs the specifications of the decay rate, bounds on the output peak, and bounds on the state-derivative feedback matrix K. These design procedures allow new specifications and also, they consider a broader class of plants than the related results available in the literature. The LMIs, when feasible, can be efficiently solved using convex programming techniques. Practical applications illustrate the efficiency of the proposed methods.

Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Well-conditioned robust observer for detection of faulty systems components

A new concept of fault detection and isolation using robust observation for systems with random noises is presented. The method selects the parameters from components that may fault during the process and constructs well conditioned robust observers, considering sensors faults. To isolate component failures via robust observation, a bank of detection observers is constructed, where each observer is only sensitive to one specified component failure while robust to all other component failures.

A barrier method for constrained nonlinear optimization using a modified Hopfield network

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel barrier method using artificial neural networks to solve robust parameter estimation problems for nonlinear model with unknown-but-bounded errors and uncertainties. This problem can be represented by a typical constrained optimization problem. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Assessing relationships between genetic evaluations using robust regression with an application to holsteins in Uruguay

Globalization of dairy cattle breeding has created a need for international sire proofs. Some early methods for converting proofs from one population to another are based on simple linear regression. An alternative robust regression method based on the t-distribution is presented, and maximum likelihood and Bayesian techniques for analysis are described, including the situation in which some proofs are missing. Procedures were used to investigate the relationship between Holstein sire proofs obtained by two Uruguayan genetic evaluation programs. The results suggest that conversion equations developed from data including only sires having proofs in both populations can lead to distorted results, relative to estimates obtained using techniques for incomplete data. There was evidence of non-normality of regression residuals, which constitutes an additional source of bias. A robust estimator may not solve all problems, but can provide simple conversion equations that are less sensitive to outlying proofs and to departures from assumptions.

Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

Robust control to parametric uncertainties in smart structures using linear matrix inequalities

The study of algorithms for active vibrations control in flexible structures became an area of enormous interest, mainly due to the countless demands of an optimal performance of mechanical systems as aircraft and aerospace structures. Smart structures, formed by a structure base, coupled with piezoelectric actuators and sensor are capable to guarantee the conditions demanded through the application of several types of controllers. This article shows some steps that should be followed in the design of a smart structure. It is discussed: the optimal placement of actuators, the model reduction and the controller design through techniques involving linear matrix inequalities (LMI). It is considered as constraints in LMI: the decay rate, voltage input limitation in the actuators and bounded output peak (output energy). Two controllers robust to parametric variation are designed: the first one considers the actuator in non-optimal location and the second one the actuator is put in an optimal placement. The performance are compared and discussed. The simulations to illustrate the methodology are made with a cantilever beam with bonded piezoelectric actuators.