There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

An Introduction to MultiAgent Systems.

https://users.encs.concordia.ca/~ymzhang/publications/ARC32-2-98Zhang_pp.229-252.pdf

Bibliographical review on reconfigurable fault-tolerant control systems

https://digital.csic.es/bitstream/10261/132943/1/water-networks.pdf

Combining CSP and MPC for the operational control of water networks

Model-based fault detection is based on generating a difference, known as a residual, between the predicted output value from the system model and the real output value measured by the sensors. If this residual is bigger than a threshold, then it is determined that there is a fault in the system. Otherwise, it is considered that the system is working properly. However, it is very important to analyse how the effect of model uncertainty is taken into account when determining the optimal threshold to be used in residual evaluation. In case that uncertainty is located in parameters (interval model), an interval observer has been shown to be a suitable strategy to generate such threshold. However, interval observers can present several problems that in order to be solved, existing approaches require computational demanding algorithms. The aim of this paper is to study the viability of using region based approaches coming from the interval analysis community to solve the interval observation problem. Region based approaches are appealing because of its low computational complexity but they suffer from the wrapping effect. On the other hand, trajectory based approaches are immune to this problem but their computational complexity is higher. In this paper, these two interval observation philosophies will be presented, analysed and compared using in two examples.

Benchmarking on approaches to interval observation applied to robust fault detection

This paper evaluates the applicability of command governor (CG) strategies to the optimal management of drinking water supply systems (DWSSs) in both centralized and distributed ways. It will be shown that CG approaches provide an adequate framework for addressing the management of these large-scale interconnected systems in the presence of periodically time-varying disturbances (water demands) that can be anticipated by using time-series forecasting approaches. The proposed centralized and distributed CG schemes are presented, discussed, and compared when applied to the management of DWSS considering the same set of operational goals in all cases. This paper illustrates the effectiveness of all strategies using the Barcelona DWSS as a case study and highlighting the advantages of each approach.

/pdf/centralized-and-distributed-command-governor-approaches-for-4cd4k37bbf.pdf

Centralized and Distributed Command Governor Approaches for Water Supply Systems Management

Fault-tolerant control (FTC) allows to preserve performance and stability despite the presence of faults The literature considers two main groups of techniques: the passive and the active FTC techniques In case of the passive techniques, the fault is taken into account as a system perturbation, so that the control law has fault capabilities that allow the system to cope with the fault presence On the other hand, in the case of the active FTC techniques, the control law uses some information given by a Fault Detection and Isolation (FDI) module, so that through some automatic adjustment in the control loop, the fault is tolerated with minimum performance degradation In this paper, a linear parameter-varying (LPV)/linear matrix inequalities (LMIs)-based technique is used to achieve fault tolerance and to compare benefits and drawbacks of passive and active FTC The proposed approach is applied to a two-wheel differential robot

/pdf/passive-and-active-ftc-comparison-for-polytopic-lpv-systems-8trhqwffvo.pdf

Passive and active FTC comparison for polytopic LPV systems

In this paper, a Fault Tolerant Control (FTC) strategy using a virtual sensor for Linear Parameter Varying (LPV) systems is proposed. The main idea of this FTC method is to reconfigure the control loop such that the nominal controller could still be used without need of retuning it. The plant with the faulty sensor is modified adding the virtual sensor block that masks the sensor fault. The suggested strategy is an active FTC strategy that reconfigures the virtual sensor on-line taking into account faults and operating point changes. In order to implement the virtual sensor approach, a fault estimation is required. Here, this fault estimation is provided by formulating it as a parameter estimation problem. Then, a block/batch least square approach is used to estimate additive and multiplicative faults. The LPV virtual sensor is designed using polytopic LPV techniques and Linear Matrix Inequalities (LMIs). To assess the performance of the proposed approach a two degree of freedom helicopter simulator is used.

/pdf/fault-estimation-and-virtual-sensor-ftc-approach-for-lpv-ubr594vzle.pdf

Vicenç Puig

Papers

Combining CSP and MPC for the operational control of water networks

Benchmarking on approaches to interval observation applied to robust fault detection

Centralized and Distributed Command Governor Approaches for Water Supply Systems Management

Passive and active FTC comparison for polytopic LPV systems

Fault estimation and virtual sensor FTC approach for LPV systems