Variable neural networks for adaptive control of nonlinear systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time, according to specified design strategies, so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBFs in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight-adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error(s). The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated example

Some thoughts on neural network modelling of micro-abrasion-corrosion processes

There is increasing interest in the interactions of microabrasion, involving small particles of less than 10 μm in size, with corrosion. This is because such interactions occur in many environments ranging from the offshore to health care sectors. In particular, micro-abrasion-corrosion can occur in oral processing, where the abrasive components of food interacting with the acidic environment, can lead to degradation of the surface dentine of teeth. Artificial neural networks (ANNs) are computing mechanisms based on the biological brain. They are very effective in various areas such as modelling, classification and pattern recognition. They have been successfully applied in almost all areas of engineering and many practical industrial applications. Hence, in this paper an attempt has been made to model the data obtained in microabrasion-corrosion experiments on polymer/steel couple and a ceramic/lasercarb coating couple using ANN. A multilayer perceptron (MLP) neural network is applied and the results obtained from modelling the tribocorrosion processes will be compared with those obtained from a relatively new class of neural networks namely resource allocation network

Forecasting time series by means of evolutionary algorithms

Proceeding of: 8th International Conference in Parallel Problem Solving from Nature - PPSN VIII , Birmingham, UK, September 18-22, 2004.The time series forecast is a very complex problem, consisting in predicting the behaviour of a data series with only the information of the previous sequence. There is many physical and artificial phenomenon that can be described by time series. The prediction of such phenomenon could be very complex. For instance, in the case of tide forecast, unusually high tides, or sea surges, result from a combination of chaotic climatic elements in conjunction with the more normal, periodic, tidal systems associated with a particular area. Too much variables influence the behaviour of the water level. Our problem is not only to find prediction rules, we also need to discard the noise and select the representative data. Our objective is to generate a set of prediction rules. There are many methods tying to achieve good predictions. In most of the cases this methods look for general rules that are able to predict the whole series. The problem is that usually the time series has local behaviours that dont allow a good level of prediction when using general rules. In this work we present a method for finding local rules able to predict only some zones of the series but achieving better level prediction. This method is based on the evolution of set of rules genetically codified, and following the Michigan approach. For evaluating the proposal, two different domains have been used: an artificial domain widely use in the bibliography (Mackey-Glass series) and a time series corresponding to a natural phenomenon, the water level in Venice Lagoon.Investigation supported by the Spanish Ministry of Science and Technology through the TRACER project under contract TIC2002-04498-C05-

Entropy of Overcomplete Kernel Dictionaries

In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the orthogonality condition of the atoms, yielding overcomplete dictionaries with an extended number of atoms. More generally than the linear decomposition, overcomplete kernel dictionaries provide an elegant nonlinear extension by defining the atoms through a mapping kernel function (e.g., the gaussian kernel). Models based on such kernel dictionaries are used in neural networks, gaussian processes and online learning with kernels. The quality of an overcomplete dictionary is evaluated with a diversity measure the distance, the approximation, the coherence and the Babel measures. In this paper, we develop a framework to examine overcomplete kernel dictionaries with the entropy from information theory. Indeed, a higher value of the entropy is associated to a further uniform spread of the atoms over the space. For each of the aforementioned diversity measures, we derive lower bounds on the entropy. Several definitions of the entropy are examined, with an extensive analysis in both the input space and the mapped feature space.Comment: 10 page