A novel approach to modelling and exploiting uncertainty in stochastic control systems

We consider an inversion-based neurocontroller for solving control problems of uncertain nonlinear systems. Classical approaches do not use uncertainty information in the neural network models. In this paper we show how we can exploit knowledge of this uncertainty to our advantage by developing a novel robust inverse control method. Simulations on a nonlinear uncertain second order system illustrate the approach.

Neural Network Modelling with Input Uncertainty: Theory and Application

It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural network framework which accounts for input noise provided that a model of the noise process exists. In the limit where the noise process is small and symmetric it is shown, using the Laplace approximation, that this method adds an extra term to the usual Bayesian error bar which depends on the variance of the input noise process. Further, by treating the true (noiseless) input as a hidden variable, and sampling this jointly with the network’s weights, using a Markov chain Monte Carlo method, it is demonstrated that it is possible to infer the regression over the noiseless input. This leads to the possibility of training an accurate model of a system using less accurate, or more uncertain, data. This is demonstrated on both the, synthetic, noisy sine wave problem and a real problem of inferring the forward model for a satellite radar backscatter system used to predict sea surface wind vectors.

Managing uncertainty in integrated environmental modelling:the UncertWeb framework

Web-based distributed modelling architectures are gaining increasing recognition as potentially useful tools to build holistic environmental models, combining individual components in complex workflows. However, existing web-based modelling frameworks currently offer no support for managing uncertainty. On the other hand, the rich array of modelling frameworks and simulation tools which support uncertainty propagation in complex and chained models typically lack the benefits of web based solutions such as ready publication, discoverability and easy access. In this article we describe the developments within the UncertWeb project which are designed to provide uncertainty support in the context of the proposed ‘Model Web’. We give an overview of uncertainty in modelling, review uncertainty management in existing modelling frameworks and consider the semantic and interoperability issues raised by integrated modelling. We describe the scope and architecture required to support uncertainty management as developed in UncertWeb. This includes tools which support elicitation, aggregation/disaggregation, visualisation and uncertainty/sensitivity analysis. We conclude by highlighting areas that require further research and development in UncertWeb, such as model calibration and inference within complex environmental models.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Robust control of nonlinear stochastic systems by modelling conditional distributions of control signals

We introduce a novel inversion-based neuro-controller for solving control problems involving uncertain nonlinear systems that could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. In this work a novel robust inverse control approach is obtained based on importance sampling from these distributions. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The performance of the new algorithm is illustrated through simulations with example systems.

Probability distribution modelling to improve stability in nonlinear MIMO control

We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

Challenging the predictive ability of accounting techniques in modelling organizational futures

This article considers the role of accounting in organisational decision making. It challenges the rational nature of decisions made in organisations through the use of accounting models and the problems of predicting the future through the use of such models. The use of accounting in this manner is evaluated from an epochal postmodern stance. Issues raised by chaos theory and the uncertainty principle are used to demonstrate problems with the predictive ability of accounting models. The authors argue that any consideration of the predictive value of accounting needs to change to incorporate a recognition of the turbulent external environment, if it is to be of use for organisational decision making. Thus it is argued that the role of accounting as a mechanism for knowledge creation regarding the future is fundamentally flawed. We take this as a starting-point to argue for the real purpose of the use of the predictive techniques of accounting, using its ritualistic role in the context of myth creation to argue for the cultural benefits of the use of such flawed techniques.

Exchanging uncertainty: interoperable geostatistics?

Traditionally, geostatistical algorithms are contained within specialist GIS and spatial statistics software. Such packages are often expensive, with relatively complex user interfaces and steep learning curves, and cannot be easily integrated into more complex process chains. In contrast, Service Oriented Architectures (SOAs) promote interoperability and loose coupling within distributed systems, typically using XML (eXtensible Markup Language) and Web services. Web services provide a mechanism for a user to discover and consume a particular process, often as part of a larger process chain, with minimal knowledge of how it works. Wrapping current geostatistical algorithms with a Web service layer would thus increase their accessibility, but raises several complex issues. This paper discusses a solution to providing interoperable, automatic geostatistical processing through the use of Web services, developed in the INTAMAP project (INTeroperability and Automated MAPping). The project builds upon Open Geospatial Consortium standards for describing observations, typically used within sensor webs, and employs Geography Markup Language (GML) to describe the spatial aspect of the problem domain. Thus the interpolation service is extremely flexible, being able to support a range of observation types, and can cope with issues such as change of support and differing error characteristics of sensors (by utilising descriptions of the observation process provided by SensorML). XML is accepted as the de facto standard for describing Web services, due to its expressive capabilities which allow automatic discovery and consumption by ‘naive’ users. Any XML schema employed must therefore be capable of describing every aspect of a service and its processes. However, no schema currently exists that can define the complex uncertainties and modelling choices that are often present within geostatistical analysis. We show a solution to this problem, developing a family of XML schemata to enable the description of a full range of uncertainty types. These types will range from simple statistics, such as the kriging mean and variances, through to a range of probability distributions and non-parametric models, such as realisations from a conditional simulation. By employing these schemata within a Web Processing Service (WPS) we show a prototype moving towards a truly interoperable geostatistical software architecture.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

Integrating OpenMI and Uncertweb:managing uncertainty in OpenMI models

OpenMI is a widely used standard allowing exchange of data between integrated models, which has mostly been applied to dynamic, deterministic models. Within the FP7 UncertWeb project we are developing mechanisms and tools to support the management of uncertainty in environmental models. In this paper we explore the integration of the UncertWeb framework with OpenMI, to assess the issues that arise when propagating uncertainty in OpenMI model compositions, and the degree of integration possible with UncertWeb tools. In particular we develop an uncertainty-enabled model for a simple Lotka-Volterra system with an interface conforming to the OpenMI standard, exploring uncertainty in the initial predator and prey levels, and the parameters of the model equations. We use the Elicitator tool developed within UncertWeb to identify the initial condition uncertainties, and show how these can be integrated, using UncertML, with simple Monte Carlo propagation mechanisms. The mediators we develop for OpenMI models are generic and produce standard Web services that expose the OpenMI models to a Web based framework. We discuss what further work is needed to allow a more complete system to be developed and show how this might be used practically.

Enhancing the performance of intelligent control systems in the face of higher levels of complexity and uncertainty

Modern advances in technology have led to more complex manufacturing processes whose success centres on the ability to control these processes with a very high level of accuracy. Plant complexity inevitably leads to poor models that exhibit a high degree of parametric or functional uncertainty. The situation becomes even more complex if the plant to be controlled is characterised by a multivalued function or even if it exhibits a number of modes of behaviour during its operation. Since an intelligent controller is expected to operate and guarantee the best performance where complexity and uncertainty coexist and interact, control engineers and theorists have recently developed new control techniques under the framework of intelligent control to enhance the performance of the controller for more complex and uncertain plants. These techniques are based on incorporating model uncertainty. The newly developed control algorithms for incorporating model uncertainty are proven to give more accurate control results under uncertain conditions. In this paper, we survey some approaches that appear to be promising for enhancing the performance of intelligent control systems in the face of higher levels of complexity and uncertainty.

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Modulating membership grades to gain consensus for fuzzy set uncertainty values in a clinical decision support system

This paper deals with a very important issue in any knowledge engineering discipline: the accurate representation and modelling of real life data and its processing by human experts. The work is applied to the GRiST Mental Health Risk Screening Tool for assessing risks associated with mental-health problems. The complexity of risk data and the wide variations in clinicians' expert opinions make it difficult to elicit representations of uncertainty that are an accurate and meaningful consensus. It requires integrating each expert's estimation of a continuous distribution of uncertainty across a range of values. This paper describes an algorithm that generates a consensual distribution at the same time as measuring the consistency of inputs. Hence it provides a measure of the confidence in the particular data item's risk contribution at the input stage and can help give an indication of the quality of subsequent risk predictions. © 2010 IEEE.

The framework of the virtual laser tracker - A systematic approach to the assessment of error sources and uncertainty in laser tracker measurement

Laser trackers have been widely used in many industries to meet increasingly high accuracy requirements. In laser tracker measurement, it is complex and difficult to perform an accurate error analysis and uncertainty evaluation. This paper firstly reviews the working principle of single beam laser trackers and state-of- The- Art of key technologies from both industrial and academic efforts, followed by a comprehensive analysis of uncertainty sources. A generic laser tracker modelling method is formulated and the framework of the virtual tracker is proposed. The VLS can be used for measurement planning, measurement accuracy optimization and uncertainty evaluation. The completed virtual laser tracking system should take all the uncertainty sources affecting coordinate measurement into consideration and establish an uncertainty model which will behave in an identical way to the real system. © Springer-Verlag Berlin Heidelberg 2010.