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

Set-Membership Parity Space Approach for Linear Uncertain Dynamic Systems

This paper proposes a robust economic model predictive control method based on a bounded description of the demand uncertainty for optimal energy dispatch in a smart micro-grid. The proposed method considers the effect of uncertainty by tightening the system constraints along the prediction horizon. The bounds of the tightened constraints are computed offline. A periodic terminal state constraint is included in order to guarantee stability. The proposed method is simpler and faster than closed-loop min-max based approaches. The proposed approach is assessed with the help of a smart-grid consisting of some photovoltaic (PV) panels, a wind generator, a hydroelectric generator, a diesel generator, and some storage devices interconnected via two DC-buses, from which load demands can draw required energy. Load demands are uncertain, but considered as bounded.

/pdf/robust-economic-model-predictive-control-for-energy-dispatch-1tgxe7zola.pdf

Robust Economic Model Predictive Control for Energy Dispatch in Smart Micro-grids Considering Demand Uncertainty

The problem of passive robust model based fault detection of dynamic systems using interval observers has been mainly addressed checking if the measured output is inside the interval of possible estimated outputs obtained considering uncertainty on model parameters. This task could be computationally expensive. In this paper, a mixed approach consisting in determining a computationally cheaper inner approximation of the estimated output interval, based on considering only the vertices of parameter uncertainty region (forward test), is combined with a parameter consistency check when the real measured output falls outside the inner solution (backward check). The backward check is implemented using interval constraint satisfaction algorithms, which can perform efficiently in deciding if the measured output is consistent with the interval model. Finally, this approach will be tested on a gas turbine nozzle servosystem.

Passive Robust Fault Detection Using a Forward-Backward Test

This paper addresses the system identification problem, as well as its application to robust fault detection, considering parametric uncertainty and using zonotopes. As a result, a Zonotopic Recursive Least Squares (ZRLS) estimator is proposed and compared with the Setmembership (SM) approach when applied to fault detection, taking as a reference the minimum detectable fault generated in the worst-case. To illustrate the effectiveness of the proposed robust parameter estimation and fault detection methodologies, a quadruple tank process is employed 

Vicenç Puig

Papers

Set-Membership Parity Space Approach for Linear Uncertain Dynamic Systems

Robust Economic Model Predictive Control for Energy Dispatch in Smart Micro-grids Considering Demand Uncertainty

Passive Robust Fault Detection Using a Forward-Backward Test

Robust Fault Detection using Zonotopic Parameter Estimation

Adaptive Threshold Generation for Robust Fault Detection Using Interval LPV Observers