Reduced complexity set-point following in self-tuning control

An external input signal is incorporated into a self-tuning controller which, although it is based on a CARMA system model, employs a state-space framework for control law calculations. Steady-state set point following can then be accomplished even when only a recursive least squares parameter estimation scheme is used, despite the fact that the disturbance affecting the system may well be coloured.

Efficient non-linear data assimilation in geophysical fluid dynamics

New ways of combining observations with numerical models are discussed in which the size of the state space can be very large, and the model can be highly nonlinear. Also the observations of the system can be related to the model variables in highly nonlinear ways, making this data-assimilation (or inverse) problem highly nonlinear. First we discuss the connection between data assimilation and inverse problems, including regularization. We explore the choice of proposal density in a Particle Filter and show how the ’curse of dimensionality’ might be beaten. In the standard Particle Filter ensembles of model runs are propagated forward in time until observations are encountered, rendering it a pure Monte-Carlo method. In large-dimensional systems this is very inefficient and very large numbers of model runs are needed to solve the data-assimilation problem realistically. In our approach we steer all model runs towards the observations resulting in a much more efficient method. By further ’ensuring almost equal weight’ we avoid performing model runs that are useless in the end. Results are shown for the 40 and 1000 dimensional Lorenz 1995 model.

The North Atlantic jet stream under climate change and its relation to the NAO and EA patterns

This paper describes recent variations of the North Atlantic eddy-driven jet stream and analyzes the mean response of the jet to anthropogenic forcing in climate models. Jet stream changes are analyzed both using a direct measure of the near-surface westerly wind maximum and using an EOF-based approach. This allows jet stream changes to be related to the widely used leading patterns of variability: the North Atlantic Oscillation (NAO) and East Atlantic (EA) pattern. Viewed in NAO–EA state space, isolines of jet latitude and speed resemble a distorted polar coordinate system, highlighting the dependence of the jet stream quantities on both spatial patterns. Some differences in the results of the two methods are discussed, but both approaches agree on the general characteristics of the climate models. While there is some agreement between models on a poleward shift of the jet stream in response to anthropogenic forcing, there is still considerable spread between different model projections, especially in winter. Furthermore, the model responses to forcing are often weaker than their biases when compared to a reanalysis. Diagnoses of jet stream changes can be sensitive to the methodologies used, and several aspects of this are also discussed.

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Information-based data selection for ensemble data assimilation

Ensemble-based data assimilation is rapidly proving itself as a computationally-efficient and skilful assimilation method for numerical weather prediction, which can provide a viable alternative to more established variational assimilation techniques. However, a fundamental shortcoming of ensemble techniques is that the resulting analysis increments can only span a limited subspace of the state space, whose dimension is less than the ensemble size. This limits the amount of observational information that can effectively constrain the analysis. In this paper, a data selection strategy that aims to assimilate only the observational components that matter most and that can be used with both stochastic and deterministic ensemble filters is presented. This avoids unnecessary computations, reduces round-off errors and minimizes the risk of importing observation bias in the analysis. When an ensemble-based assimilation technique is used to assimilate high-density observations, the data-selection procedure allows the use of larger localization domains that may lead to a more balanced analysis. Results from the use of this data selection technique with a two-dimensional linear and a nonlinear advection model using both in situ and remote sounding observations are discussed.

Efficient fully nonlinear data assimilation for geophysical fluid dynamics

A potential problem with Ensemble Kalman Filter is the implicit Gaussian assumption at analysis times. Here we explore the performance of a recently proposed fully nonlinear particle filter on a high-dimensional but simplified ocean model, in which the Gaussian assumption is not made. The model simulates the evolution of the vorticity field in time, described by the barotropic vorticity equation, in a highly nonlinear flow regime. While common knowledge is that particle filters are inefficient and need large numbers of model runs to avoid degeneracy, the newly developed particle filter needs only of the order of 10-100 particles on large scale problems. The crucial new ingredient is that the proposal density cannot only be used to ensure all particles end up in high-probability regions of state space as defined by the observations, but also to ensure that most of the particles have similar weights. Using identical twin experiments we found that the ensemble mean follows the truth reliably, and the difference from the truth is captured by the ensemble spread. A rank histogram is used to show that the truth run is indistinguishable from any of the particles, showing statistical consistency of the method.

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of lactating dairy cows

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of the lactating dairy cow is constructed and solved in the steady state. The model contains four intracellular and four extracellular pools and conservation of mass principles are applied to generate the fundamental equations describing the behaviour of the system. The experimental measurements required for model solution are milk secretion and plasma flow rate across the gland in combination with phenylalanine and tyrosine concentrations and plateau isotopic enrichments in arterial and venous plasma and free and protein bound milk during a constant infusion of [1-(13)C]phenylalanine and [2,3,5,6-(2)H]tyrosine tracer. If assumptions are made, model solution enables determination of steady state flows for phenylalanine and tyrosine inflow to the gland, outflow from it and bypass, and flows representing the synthesis and degradation of constitutive protein and hydroxylation. The model is effective in providing information about the fates of phenylalanine and tyrosine in the mammary gland and could be used as part of a more complex system describing amino acid metabolism in the whole ruminant.

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

The global response to tropical heating in the Madden-Julian oscillation during the northern winter

A life cycle of the Madden–Julian oscillation (MJO) was constructed, based on 21 years of outgoing long-wave radiation data. Regression maps of NCEP–NCAR reanalysis data for the northern winter show statistically significant upper-tropospheric equatorial wave patterns linked to the tropical convection anomalies, and extratropical wave patterns over the North Pacific, North America, the Atlantic, the Southern Ocean and South America. To assess the cause of the circulation anomalies, a global primitive-equation model was initialized with the observed three-dimensional (3D) winter climatological mean flow and forced with a time-dependent heat source derived from the observed MJO anomalies. A model MJO cycle was constructed from the global response to the heating, and both the tropical and extratropical circulation anomalies generally matched the observations well. The equatorial wave patterns are established in a few days, while it takes approximately two weeks for the extratropical patterns to appear. The model response is robust and insensitive to realistic changes in damping and basic state. The model tropical anomalies are consistent with a forced equatorial Rossby–Kelvin wave response to the tropical MJO heating, although it is shifted westward by approximately 20° longitude relative to observations. This may be due to a lack of damping processes (cumulus friction) in the regions of convective heating. Once this shift is accounted for, the extratropical response is consistent with theories of Rossby wave forcing and dispersion on the climatological flow, and the pattern correlation between the observed and modelled extratropical flow is up to 0.85. The observed tropical and extratropical wave patterns account for a significant fraction of the intraseasonal circulation variance, and this reproducibility as a response to tropical MJO convection has implications for global medium-range weather prediction. Copyright © 2004 Royal Meteorological Society

Mapping and controlling molecular processes: The application of control theory and system identification algorithms to ASOPS and other fast pulse spectroscopies

Asynchronous Optical Sampling (ASOPS) [1,2] and frequency comb spectrometry [3] based on dual Ti:saphire resonators operated in a master/slave mode have the potential to improve signal to noise ratio in THz transient and IR sperctrometry. The multimode Brownian oscillator time-domain response function described by state-space models is a mathematically robust framework that can be used to describe the dispersive phenomena governed by Lorentzian, Debye and Drude responses. In addition, the optical properties of an arbitrary medium can be expressed as a linear combination of simple multimode Brownian oscillator functions. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing the recorded THz transients in the time or frequency domain will be outlined [4,5]. Since a femtosecond duration pulse is capable of persistent excitation of the medium within which it propagates, such approach is perfectly justifiable. Several de-noising routines based on system identification will be shown. Furthermore, specifically developed apodization structures will be discussed. These are necessary because due to dispersion issues, the time-domain background and sample interferograms are non-symmetrical [6-8]. These procedures can lead to a more precise estimation of the complex insertion loss function. The algorithms are applicable to femtosecond spectroscopies across the EM spectrum. Finally, a methodology for femtosecond pulse shaping using genetic algorithms aiming to map and control molecular relaxation processes will be mentioned.

Optimal foraging when regulating intake of multiple nutrients

There is growing evidence that, rather than maximizing energy intake subject to constraints, many animals attempt to regulate intake of multiple nutrients independently. In the complex diets of animals such as herbivores, the consumption of nutritionally imbalanced foods is sometimes inevitable, forcing trade-offs between eating too much of nutrients present in the foods in relative excess against too little of those in deficit. Such situations are not adequately represented in existing formulations of foraging theory. Here we provide the necessary theory to fit this case, using an approach that combines state-space models of nutrition with Tilman's models of resource exploitation (Tilman 1982, Resource Competition and Community Structure, Princeton: Princeton University Press). Our approach was to construct a smooth fitness landscape over nutrient space, centred on a 'target' intake at which no fitness cost is incurred, and this leads to a natural classification of the simple possible fitness landscapes based on Taylor series approximations of landscape shape. We next examined how needs for multiple nutrients can be assessed experimentally using direct measures of animal performance as the common currency, so that the nutritional strategies of animals can be mapped on to the performance surface, including the position of regulated points of intake and points of nutrient balance when fed suboptimal foods. We surveyed published data and conducted an experiment to map out the performance landscape of a generalist leaf-feeding caterpillar, Spodoptera littoralis. (C) 2004 Tire Association for the Study of Animal Behaviour. Poblished by Elsevier Ltd. All rights reserved.

Filtering techniques in self-tuning

In the last few years a state-space formulation has been introduced into self-tuning control. This has not only allowed for a wider choice of possible control actions, but has also provided an insight into the theory underlying—and hidden by—that used in the polynomial description. This paper considers many of the self-tuning algorithms, both state-space and polynomial, presently in use, and by starting from first principles develops the observers which are, effectively, used in each case. At any specific time instant the state estimator can be regarded as taking one of two forms. In the first case the most recently available output measurement is excluded, and here an optimal and conditionally stable observer is obtained. In the second case the present output signal is included, and here it is shown that although the observer is once again conditionally stable, it is no longer optimal. This result is of significance, as many of the popular self-tuning controllers lie in the second, rather than first, category.

Using self-organising feature maps for the control of artificial organisms

Variations on the standard Kohonen feature map can enable an ordering of the map state space by using only a limited subset of the complete input vector. Also it is possible to employ merely a local adaptation procedure to order the map, rather than having to rely on global variables and objectives. Such variations have been included as part of a hybrid learning system (HLS) which has arisen out of a genetic-based classifier system. In the paper a description of the modified feature map is given, which constitutes the HLSs long term memory, and results in the control of a simple maze running task are presented, thereby demonstrating the value of goal related feedback within the overall network.

Control strategy for Boolean input systems

The purpose of this paper is to design a control law for continuous systems with Boolean inputs allowing the output to track a desired trajectory. Such systems are controlled by items of commutation. This type of systems, with Boolean inputs, has found increasing use in the electric industry. Power supplies include such systems and a power converter represents one of theses systems. For instance, in power electronics the control variable is the switching OFF and ON of components such as thyristors or transistors. In this paper, a method is proposed for the designing of a control law in state space for such systems. This approach is implemented in simulation for the control of an electronic circuit.

A practical approach for training dynamic recurrent neural networks: use of Apriori information

Presents a technique for incorporating a priori knowledge from a state space system into a neural network training algorithm. The training algorithm considered is that of chemotaxis and the networks being trained are recurrent neural networks. Incorporation of the a priori knowledge ensures that the resultant network has behaviour similar to the system which it is modelling.