Internal model control of nonlinear systems through the inversion of recurrent neural networks

Recurrent neural networks can be used for both the identification and control of nonlinear systems. This paper takes a previously derived set of theoretical results about recurrent neural networks and applies them to the task of providing internal model control for a nonlinear plant. Using the theoretical results, we show how an inverse controller can be produced from a neural network model of the plant, without the need to train an additional network to perform the inverse control.

Identification of nonlinear systems with a dynamic recurrent neural network

Two approaches are presented to calculate the weights for a Dynamic Recurrent Neural Network (DRNN) in order to identify the input-output dynamics of a class of nonlinear systems. The number of states of the identified network is constrained to be the same as the number of states of the plant.

A titration model: an analysis and solution

The Newton‐Raphson method is proposed for the solution of the nonlinear equation arising from a theoretical model of an acid/base titration. It is shown that it is necessary to modify the form of the equation in order that the iteration is guaranteed to converge. A particular example is considered to illustrate the analysis and method, and a BASIC program is included that can be used to predict the pH of any weak acid/weak base titration.

Nonlinear data assimilation in geosciences: an extremely efficient particle filter

Almost all research fields in geosciences use numerical models and observations and combine these using data-assimilation techniques. With ever-increasing resolution and complexity, the numerical models tend to be highly nonlinear and also observations become more complicated and their relation to the models more nonlinear. Standard data-assimilation techniques like (ensemble) Kalman filters and variational methods like 4D-Var rely on linearizations and are likely to fail in one way or another. Nonlinear data-assimilation techniques are available, but are only efficient for small-dimensional problems, hampered by the so-called ‘curse of dimensionality’. Here we present a fully nonlinear particle filter that can be applied to higher dimensional problems by exploiting the freedom of the proposal density inherent in particle filtering. The method is illustrated for the three-dimensional Lorenz model using three particles and the much more complex 40-dimensional Lorenz model using 20 particles. By also applying the method to the 1000-dimensional Lorenz model, again using only 20 particles, we demonstrate the strong scale-invariance of the method, leading to the optimistic conjecture that the method is applicable to realistic geophysical problems. Copyright c 2010 Royal Meteorological Society

The influence of the carbon surface chemical composition on Dubinin-Astakhov equation parameters calculated from SF(6) adsorption data-grand canonical Monte Carlo simulation

Using grand canonical Monte Carlo simulation we show, for the first time, the influence of the carbon porosity and surface oxidation on the parameters of the Dubinin-Astakhov (DA) adsorption isotherm equation. We conclude that upon carbon surface oxidation, the adsorption decreases for all carbons studied. Moreover, the parameters of the DA model depend on the number of surface oxygen groups. That is why in the case of carbons containing surface polar groups, SF(6) adsorption isotherm data cannot be used for characterization of the porosity.