Abstract
This article presents an optimal estimator for discrete-time systems disturbed by output white noise, where the proposed algorithm identifies the parameters of a Multiple Input Single Output LPV State Space model. This is an LPV version of a class of algorithms proposed elsewhere for identifying LTI systems. These algorithms use the matchable observable linear identification parameterization that leads to an LTI predictor in a linear regression form, where the ouput prediction is a linear function of the unknown parameters. With a proper choice of the predictor parameters, the optimal prediction error estimator can be approximated. In a previous work, an LPV version of this method, that also used an LTI predictor, was proposed; this LTI predictor was in a linear regression form enablin, in this way, the model estimation to be handled by a Least-Squares Support Vector Machine approach, where the kernel functions had to be filtered by an LTI 2D-system with the predictor dynamics. As a result, it can never approximate an optimal LPV predictor which is essential for an optimal prediction error LPV estimator. In this work, both the unknown parameters and the state-matrix of the output predictor are described as a linear combination of a finite number of basis functions of the scheduling signal; the LPV predictor is derived and it is shown to be also in the regression form, allowing the unknown parameters to be estimated by a simple linear least squares method. Due to the LPV nature of the predictor, a proper choice of its parameters can lead to the formulation of an optimal prediction error LPV estimator. Simulated examples are used to assess the effectiveness of the algorithm. In future work, optimal prediction error estimators will be derived for more general disturbances and the LPV predictor will be used in the Least-Squares Support Vector Machine approach.

Abstract
This article presents four state-space models for high pressure gas pipelines, departing from a system of nonlinear partial differential equations. The models were derived taking advantage of an electrical analogy and are very accurate and simple, therefore suitable for network simulation and analysis. The models' simulation is compared with the data obtained with Simone (R), a commercial simulator of gas transport and distribution networks used by many european companies, and exhibit similar accuracy.

Abstract
While most physical systems or phenomena occur in continuous-time, identification methods based on discrete-time models are more widespread among practitioners and academic community, possibly due to the discrete-time nature of the data records. There has been a growing interest in estimating continuous-time (CT) models in the last decade. This work develops algorithms to estimate the parameters of multivariable state-space CT models from input-output samples using a method based on the recently developed MOLI-ZOFT approach. The performance of the algorithm is evaluated using real data from an industrial winding process.

Abstract
A cost-effective, accurate, and robust leak detection method is essential in gas network management in order to reduce inspection time and to increase reliability in the system. This work presents a model-based leakage detection method; the gas dynamics are described by a linearized system of partial differential equations that is further reduced to a one-dimensional spatial model. By using an electrical analogy, a pipeline can be represented by a two-port network, where mass flow behaves like current and pressure like voltage. Four transfer function quadripole models are then established to describe the gas pipeline dynamics, depending on the variables of interest at the pipeline boundaries. A leak detection method is devised by employing mass flow data at boundaries and pressure data at some point of the pipeline, as well as by assessing the effects of the leakage on the pressure and mass flow along the pipeline. A case study has been built from operational data supplied by REN Gasodutos (the Portuguese gas company) to show the advantages of the proposed models. © Springer International Publishing AG 2017.

Abstract
A system identification approach is used estimate linear time invariant models from the data of physical activity gathered in the Just Walk intervention conducted by the Designing Health Lab and the Control Systems Laboratory at Arizona State University A class of identification algorithms proposed elsewhere by one of the authors, denoted as MoliZoft, was reformulated and adapted to estimate models from data gathered in this experience. In this paper, the identification algorithms are described and the best models estimated for a particular participant are analysed and used to improve the results in future experiments.

Abstract
In this paper we design a model based method to locate a leakage and estimate its size in a gas network, using a linearised version of an hyperbolic PDE. To do this, the problem is reduced to two identical ODEs, allowing in this way for a representation of the pressure as well as the mass flow in terms of its system of fundamental solutions. Then using the available measurements at the grid boundary points, the correspondent coefficients can be determined. Assuming pressure continuity, we check for consistency of the coefficients in order to find faulty pipelines. Thence, the location of the leakage can be found either graphically or using a numerical method for a specific pipe. Next, its size can also be estimated. © Springer International Publishing Switzerland 2017.