H∞ robust control design for unsupported paraplegic standing: experimental evaluation

This paper is concerned with the design of robust feedback H~-control systems for the control of the upright posture of paraplegic persons standing. While the subject stands in a special apparatus, stabilising torque at the ankle joint is generated by electrical stimulation of the paralyzed calf muscles. Since the muscles acting as actuators in this setup show a significant degree of nonlinearity, a robust H~-control design is used. The design approach is implemented in experiments with a paraplegic subject. The results demonstrate good performance and closed loop stability over the whole range of operation.

Aldose reductase and the importance of experimental design

Kinetic studies on the AR (aldose reductase) protein have shown that it does not behave as a classical enzyme in relation to ring aldose sugars. As with non-enzymatic glycation reactions, there is probably a free radical element involved derived from monosaccharide autoxidation. in the case of AR, there is free radical oxidation of NADPH by autoxidizing monosaccharides, which is enhanced in the presence of the NADPH-binding protein. Thus any assay for AR based on the oxidation of NADPH in the presence of autoxidizing monosaccharides is invalid, and tissue AR measurements based on this method are also invalid, and should be reassessed. AR exhibits broad specificity for both hydrophilic and hydrophobic aldehydes that suggests that the protein may be involved in detoxification. The last thing we would want to do is to inhibit it. ARIs (AR inhibitors) have a number of actions in the cell which are not specific, and which do not involve them binding to AR. These include peroxy-radical scavenging and effects of metal ion chelation. The AR/ARI story emphasizes the importance of correct experimental design in all biocatalytic experiments. Developing the use of Bayesian utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has led to the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K-m and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimizes the error in the parameters estimated, and is suitable for simple or complex steady-state models.

Efficient and accurate experimental design for enzyme kinetics: Bayesian studies reveal a systematic approach

In areas such as drug development, clinical diagnosis and biotechnology research, acquiring details about the kinetic parameters of enzymes is crucial. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. We demonstrate that a Bayesian approach (the use of prior knowledge) can produce major gains quantifiable in terms of information, productivity and accuracy of each experiment. Developing the use of Bayesian Utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has enabled the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K-M and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. (C) 2003 Elsevier Science B.V. All rights reserved.

Sparse kernel density estimator using orthogonal regression based on D-optimality experimental design

A novel sparse kernel density estimator is derived based on a regression approach, which selects a very small subset of significant kernels by means of the D-optimality experimental design criterion using an orthogonal forward selection procedure. The weights of the resulting sparse kernel model are calculated using the multiplicative nonnegative quadratic programming algorithm. The proposed method is computationally attractive, in comparison with many existing kernel density estimation algorithms. Our numerical results also show that the proposed method compares favourably with other existing methods, in terms of both test accuracy and model sparsity, for constructing kernel density estimates.

Sparse multioutput radial basis function network construction using combined locally regularised orthogonal least square and D-optimality experimental design

A construction algorithm for multioutput radial basis function (RBF) network modelling is introduced by combining a locally regularised orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximised model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious RBF network model with excellent generalisation performance. The D-optimality design criterion enhances the model efficiency and robustness. A further advantage of the combined approach is that the user only needs to specify a weighting for the D-optimality cost in the combined RBF model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.

Sparse kernel regression modeling using combined locally regularized orthogonal least squares and D-optimality experimental design

The note proposes an efficient nonlinear identification algorithm by combining a locally regularized orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious model with excellent generalization performance. The D-optimality design criterion further enhances the model efficiency and robustness. An added advantage is that the user only needs to specify a weighting for the D-optimality cost in the combined model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.

Experimental design and model construction algorithms for radial basis function networks

New construction algorithms for radial basis function (RBF) network modelling are introduced based on the A-optimality and D-optimality experimental design criteria respectively. We utilize new cost functions, based on experimental design criteria, for model selection that simultaneously optimizes model approximation, parameter variance (A-optimality) or model robustness (D-optimality). The proposed approaches are based on the forward orthogonal least-squares (OLS) algorithm, such that the new A-optimality- and D-optimality-based cost functions are constructed on the basis of an orthogonalization process that gains computational advantages and hence maintains the inherent computational efficiency associated with the conventional forward OLS approach. The proposed approach enhances the very popular forward OLS-algorithm-based RBF model construction method since the resultant RBF models are constructed in a manner that the system dynamics approximation capability, model adequacy and robustness are optimized simultaneously. The numerical examples provided show significant improvement based on the D-optimality design criterion, demonstrating that there is significant room for improvement in modelling via the popular RBF neural network.

Regression based D-optimality experimental design for sparse kernel density estimation

This paper derives an efficient algorithm for constructing sparse kernel density (SKD) estimates. The algorithm first selects a very small subset of significant kernels using an orthogonal forward regression (OFR) procedure based on the D-optimality experimental design criterion. The weights of the resulting sparse kernel model are then calculated using a modified multiplicative nonnegative quadratic programming algorithm. Unlike most of the SKD estimators, the proposed D-optimality regression approach is an unsupervised construction algorithm and it does not require an empirical desired response for the kernel selection task. The strength of the D-optimality OFR is owing to the fact that the algorithm automatically selects a small subset of the most significant kernels related to the largest eigenvalues of the kernel design matrix, which counts for the most energy of the kernel training data, and this also guarantees the most accurate kernel weight estimate. The proposed method is also computationally attractive, in comparison with many existing SKD construction algorithms. Extensive numerical investigation demonstrates the ability of this regression-based approach to efficiently construct a very sparse kernel density estimate with excellent test accuracy, and our results show that the proposed method compares favourably with other existing sparse methods, in terms of test accuracy, model sparsity and complexity, for constructing kernel density estimates.

Nonlinear model structure detection using optimum experimental design and orthogonal least squares

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the subset selection cost function includes an A-optimality design criterion to minimize the variance of the parameter estimates that ensures the adequacy and parsimony of the final model. An illustrative example is included to demonstrate the effectiveness of the new approach.

A robust controller design method for feedback substitution schemes using genetic algorithms

Controllers for feedback substitution schemes demonstrate a trade-off between noise power gain and normalized response time. Using as an example the design of a controller for a radiometric transduction process subjected to arbitrary noise power gain and robustness constraints, a Pareto-front of optimal controller solutions fulfilling a range of time-domain design objectives can be derived. In this work, we consider designs using a loop shaping design procedure (LSDP). The approach uses linear matrix inequalities to specify a range of objectives and a genetic algorithm (GA) to perform a multi-objective optimization for the controller weights (MOGA). A clonal selection algorithm is used to further provide a directed search of the GA towards the Pareto front. We demonstrate that with the proposed methodology, it is possible to design higher order controllers with superior performance in terms of response time, noise power gain and robustness.

High-resolution global climate simulations with the ECMWF model in Project Athena: experimental design, model climate, and seasonal forecast skill

The sensitivity to the horizontal resolution of the climate, anthropogenic climate change, and seasonal predictive skill of the ECMWF model has been studied as part of Project Athena—an international collaboration formed to test the hypothesis that substantial progress in simulating and predicting climate can be achieved if mesoscale and subsynoptic atmospheric phenomena are more realistically represented in climate models. In this study the experiments carried out with the ECMWF model (atmosphere only) are described in detail. Here, the focus is on the tropics and the Northern Hemisphere extratropics during boreal winter. The resolutions considered in Project Athena for the ECMWF model are T159 (126 km), T511 (39 km), T1279 (16 km), and T2047 (10 km). It was found that increasing horizontal resolution improves the tropical precipitation, the tropical atmospheric circulation, the frequency of occurrence of Euro-Atlantic blocking, and the representation of extratropical cyclones in large parts of the Northern Hemisphere extratropics. All of these improvements come from the increase in resolution from T159 to T511 with relatively small changes for further resolution increases to T1279 and T2047, although it should be noted that results from this very highest resolution are from a previously untested model version. Problems in simulating the Madden–Julian oscillation remain unchanged for all resolutions tested. There is some evidence that increasing horizontal resolution to T1279 leads to moderate increases in seasonal forecast skill during boreal winter in the tropics and Northern Hemisphere extratropics. Sensitivity experiments are discussed, which helps to foster a better understanding of some of the resolution dependence found for the ECMWF model in Project Athena

A slugfest of intuitions: contextualism and experimental design

This paper considers ways that experimental design can affect judgments about informally presented context shifting experiments. Reasons are given to think that judgments about informal context shifting experiments are affected by an exclusive reliance on binary truth value judgments and by experimenter bias. Exclusive reliance on binary truth value judgments may produce experimental artifacts by obscuring important differences of degree between the phenomena being investigated. Experimenter bias is an effect generated when, for example, experimenters disclose (even unconsciously) their own beliefs about the outcome of an experiment. Eliminating experimenter bias from context shifting experiments makes it far less obvious what the “intuitive” responses to those experiments are. After it is shown how those different kinds of bias can affect judgments about informal context shifting experiments, those experiments are revised to control for those forms of bias. The upshot of these investigations is that participants in the contextualist debate who employ informal experiments should pay just as much attention to the design of their experiments as those who employ more formal experimental techniques if they want to avoid obscuring the phenomena they aim to uncover

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Robust nonlinear model identification methods using forward regression

In this correspondence new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness via combined parameter regularization and new robust structural selective criteria. In parallel to parameter regularization, we use two classes of robust model selection criteria based on either experimental design criteria that optimizes model adequacy, or the predicted residual sums of squares (PRESS) statistic that optimizes model generalization capability, respectively. Three robust identification algorithms are introduced, i.e., combined A- and D-optimality with regularized orthogonal least squares algorithm, respectively; and combined PRESS statistic with regularized orthogonal least squares algorithm. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalization scheme in orthogonal least squares or regularized orthogonal least squares has been extended such that the new algorithms are computationally efficient. Numerical examples are included to demonstrate effectiveness of the algorithms.

Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.