Abstract
In this paper, the gas dynamics within the pipelines is modelled as a repetitive process with smoothing. Controllability and observability criteria when the system is steered through initial and boundary data, which is achieved by an adequate choice of the homogeneity, are obtained. From the point of view of the technical applications, it seems to make more sense to consider boundary data controls as for instance in the management of high pressure gas networks. Stability criteria suitable computer simulations are also included.

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
In this article, an algorithm to identify LPV State Space models is proposed. The LPV State Space system is in the companion reachable canonical form. Both the state matrix and the output vector coefficients are linear combinations of a set of nonlinear basis functions dependent on the scheduling signal. This model structure, although simple, can describe accurately the behaviour of many nonlinear systems by an adequate choice of the scheduling signal. The identification algorithm minimises a quadratic criterion of the output error. Since this error is a linear function of the output vector parameters, a separable nonlinear least squares approach is used to minimise the criterion function by a gradient method. The derivatives required by the algorithm are the states of LPV systems that need to be simulated at every iteration. The effectiveness of the algorithm is assessed by two simulated examples.

Abstract
In this paper we introduce a bilinear repetitive process and present an iterative subspace algorithm for its identification. The advantage of the proposed approach is that it overcomes the "curse of dimensionality", a hurdle commonly encountered with classical bilinear subspace identification algorithms. Simulation results show that the algorithm converges quickly and provides new alternatives for modeling/identifying nonlinear repetitive processes.

Abstract
In this paper, the gas dynamics within the pipelines is written as a wave repetitive process, and modify it in a way that the dynamics is influenced by p decision makers, namely the boundary conditions. We obtain sufficient criteria for the existence of boundary equilibrium controls as well as controllability of the different agents and observability of the system when this is steered through initial and boundary data. From the point of view of some applications it seems to make sense to consider boundary data controls, e.g. in high pressure gas networks management.

Abstract
There is good evidence that naltrexone, an opioid antagonist, has a strong neuroprotective role and may be a potential drug for the treatment of fibromyalgia. In previous work, some of the authors used experimental clinical data to identify input-output linear time invariant models that were used to extract useful information about the effect of this drug on fibromyalgia symptoms. Additional factors such as anxiety, stress, mood, and headache, were considered as additive disturbances. However, it seems reasonable to think that these factors do not affect the drug actuation, but only the way in which a participant perceives how the drug actuates on herself. Under this hypothesis the linear time invariant models can be replaced by State-Space Affine Linear Parameter Varying models where the disturbances are seen as a scheduling signal signal only acting at the parameters of the output equation. In this paper a new algorithm for identifying such a model is proposed. This algorithm minimizes a quadratic criterion of the output error. Since the output error is a linear function of some parameters, the Affine Linear Parameter Varying system identification is formulated as a separable nonlinear least squares problem. Likewise other identification algorithms using gradient optimization methods several parameter derivatives are dynamical systems that must be simulated. In order to increase time efficiency a canonical parametrization that minimizes the number of systems to be simulated is chosen. The effectiveness of the algorithm is assessed in a case study where an Affine Parameter Varying Model is identified from the experimental data used in the previous study and compared with the time-invariant model.