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This is the peer reviewed version of the following article: Diez, P. [et al.]. Nonlinear dimensionality reduction for parametric problems: a kernel proper orthogonal decomposition. "International journal for numerical methods in engineering", 30 Desembre 2021, vol. 122, núm. 24, p. 7306-7327, which has been published in final form at DOI: 10.1002/nme.6831. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with dimension equal to the number of independent parameters) embedded in a large-dimensional space (dimension equal to the number of degrees of freedom of the full-order discrete model). A posteriori model reduction is based on constructing a basis from a family of snapshots (solutions of the full-order model computed offline), and then use this new basis to solve the subsequent instances online. Proper orthogonal decomposition (POD) reduces the problem into a linear subspace of lower dimension, eliminating redundancies in the family of snapshots. The strategy proposed here is to use a nonlinear dimensionality reduction technique, namely, the kernel principal component analysis (kPCA), in order to find a nonlinear manifold, with an expected much lower dimension, and to solve the problem in this low-dimensional manifold. Guided by this paradigm, the methodology devised here introduces different novel ideas, namely, 1) characterizing the nonlinear manifold using local tangent spaces, where the reduced-order problem is linear and based on the neighboring snapshots, 2) the approximation space is enriched with the cross-products of the snapshots, introducing a quadratic description, 3) the kernel for kPCA is defined ad hoc, based on physical considerations, and 4) the iterations in the reduced-dimensional space are performed using an algorithm based on a Delaunay tessellation of the cloud of snapshots in the reduced space. The resulting computational strategy is performing outstandingly in the numerical tests, alleviating many of the problems associated with POD and improving the numerical accuracy. Generalitat de Catalunya, 2017-SGR-1278; Ministerio de Ciencia e Innovación, CEX2018-000797-S; PID2020-113463RB-C32; PID2020-113463RB-C33

The notion of Control in Complex Systems has started almost 60 years ago by Kalman. However, the results obtained were not sufficient for systems with complex topologies (Complex Networks) and non-linear dynamics. Thanks to many works and especially the one of Liu et.al. on 2011, the topic of Control in Complex networks has returned to the forefront and has been studied intensively during the last decade. Big progress has been made, but still there are many different aspects unsolved in the area. Different notions like structural controllability or required energy to control a network have been imported, but a unifying framework between Complex Systems and Control Theory is still missing, as non-linearity, complexity and dimensionality make it difficult and very often infeasible to extract general and unifying conclusions about this kind of systems. In this work we explore the dynamical properties of the Kuramoto model, focusing the theoretical analysis on the Star-Graph topology taking into consideration the original Kuramoto model, as well as a perturbed expansion of it. Then, a candidate control Lyapunov function is proposed and together with the rest of the theoretical results, is validated by performing various numerical simulations and deploying Model Predictive Control for the controlled cases.

© 2022 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Searching for achieving an ambitious reduction in greenhouse gas emissions, the EU has set as a goal a modal shift in freight transport of 30% by rail for the near future. In this context, it is vital to use modal choice models road versus rail to assess the shippers' acceptance of the actions promoting the use of rail. This paper develops a combined model for jointly evaluating modal split and railway freight ows, addressed to the case when a modal split based on a random utility model is available, and some of its coe -cients may present a non-negligible variability. To this end, after the initial deterministic formulation a robust counterpart of the model is developed. The model, formulated as a non-linear integer programming problem, is oriented to a multi-carrier environment and includes constraints to consider the interactions between the di erent types of ows on the railway network, allowing a good evaluation of the cost types of the carriers and the network capacity. An algorithmic solution based on the outer approximation method is shown to provide accurate solutions in a reasonable computational time for the robust and non-robust versions of the model. Examples centered on a section of the Trans-European Transport Network, the TEN-T Core network corridors, are reported to test the model's applicability. Results show that this model can be a helpful tool for analyzing the possible shippers' response to the di erent railway carriers' services competing with the road.

Renewable and distributed energy sources, with photovoltaic in the first place, are leading the energy transition. However, they alone will hardly find the way to success in this challenge because of their intrinsic limitations, such as their dependency on weather condition and the unpredictability of their production. Demand Response services are considered crucial for the integration of renewable sources in the grid. This study presents a methodology to evaluate potential flexibility in commercial buildings by managing air conditioning and lighting systems of the site. The study proposes two different data-driven approaches to evaluate flexibility depending on the technology considered. For lighting systems, flexibility is evaluated using the XGBoost classification algorithm combined with a piecewise function. The thermal behavior of the building is modeled with a simplified RC equivalent state-space model. For both algorithms, preprocessing showed to be a critical part of the process, which is explained stage-by-stage in the paper. Results show that the lighting flexibility algorithm is very reliable, reaching an average error of less than 1 % during the months considered. The simplified thermal modeling proposed shows promising results, having less than 0.2 o C of RMSE error for the internal temperature forecast. In addition, results show the flexibility potentiality of the building, which is potentially able to shift up to 23 % of its power consumption during certain hours of the day. This opens huge opportunities for taking advantage from dynamic tariffs, increase self-consumption from renewable sources or participate in flexibility markets to reduce buildings' electricity bill and help renewable integration.

This paper analyzes the behavior of a miniature 3D wind sensor designed for Mars atmosphere. The sensor is a spherical structure of 10 mm diameter divided in four sectors. By setting all the sectors to constant temperature, above that of the air, the 3D wind velocity vector can be measured. Two sets of experiments have been performed. First, an experimental campaign made under typical Mars conditions at the Aarhus Wind Tunnel Simulator is presented. The results demonstrate that both wind speed and angle can be efficiently measured, using a simple inverse algorithm. The effect of sudden wind changes is also analyzed and fast response times in the range of 0.7 s are obtained. The second set of experiments is focused on analyzing the performance of the sensor under extreme Martian wind conditions, reaching and going beyond the Dust Devil scale. To this purpose, both high-fidelity numerical simulations of fluid dynamics and heat transfer and experiments with the sensor have been performed. The results of the experiments, made for winds in the Reynolds number 1000&ndash, 2000 range, which represent 65&ndash, 130 m/s of wind speed under typical Mars conditions, further confirm the simulation predictions and show that it will be possible to successfully measure wind speed and direction even under these extreme regimes.

The main objective of this study was to introduce a survival model to contemplate two simultaneous accelerating factors affecting a food product's shelf life: temperature and illumination. A second objective was to consider the case where the same consumer tests different experimental conditions and thus his/her data are not independent. Sample data comprised 108 consumers who evaluated a lemon-flavored juice stored at 24 °C, 37 °C and 45 °C; under conditions of no-illumination and with illumination; with seven different storage times for each of the six experimental conditions. Aiming to estimate the storage time at which a consumer rejects a sample a model including an Arrhenius term for the temperature, a binomial response for illumination (with and without) and the interaction of both was developed. The model also considered that the same consumer tested different experimental conditions. Fil: Garitta, Lorena Garitta. Provincia de Buenos Aires. Dirección General de Cultura y Educación. Instituto Superior Experimental de Tecnología Alimentaria; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Langohr, Klaus. Universidad Politécnica de Catalunya; España Fil: Elizagoyen, Eliana Soledad. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina. Provincia de Buenos Aires. Dirección General de Cultura y Educación. Instituto Superior Experimental de Tecnología Alimentaria; Argentina Fil: Gugole Ottaviano, Maria Fernanda. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Provincia de Buenos Aires. Dirección General de Cultura y Educación. Instituto Superior Experimental de Tecnología Alimentaria; Argentina Fil: Gómez, Guadalupe. Universidad Politécnica de Catalunya; España Fil: Hough, Guillermo. Provincia de Buenos Aires. Dirección General de Cultura y Educación. Instituto Superior Experimental de Tecnología Alimentaria; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina

Large aeronautical structural parts present important distortions after machining. This problem is caused by the presence of residual stresses, which are developed during previous manufacturing steps (quenching). Before being put into service, the nominal geometry is restored by means of mechanical methods. This operation is called reshaping and exclusively depends on the skills of a well-trained and experienced operator. Moreover, this procedure is time consuming and nowadays, it is only based on a trial and error approach. Therefore, there is a need at industrial level to solve this problem with the support of numerical simulation tools. By using a simplification hypothesis, it was found that the springback phenomenon behaves linearly and it allows developing a strategy to implement reshaping at an industrial level. © 2018 Author(s).

In this work, a coordinate change of state variables is performed for drift-less systems of dimension m+2 with 2 inputs using Goursat Normal Form. Then, we define a feedback law that will allow us to convert the original system into chained form. Later on, we find the flat outputs and define a new feedback law. Finally, numerical simulations are presented for a planar space robot, a mobile robot with a trailer and a N-trailer.

The compilation of results involving feedback linearization and the computation of flat outputs within the framework of exterior differential systems are the focus of our work.

Institut de Robòtica i Informàtica Industrial (CSIC-UPC) Mesurar la proximitat a les configuracions singulars dels manipuladors paral·lels pot ser útil per evitar el mal comportament que es dóna quan el manipulador es mou en un entorn d'una singularitat. Alguns dels índexos que s'han introduït fins ara que podrien resoldre aquest problema són poc adequats. En aquest projecte tecnològic s'introdueixen dos nous índexos que són una solució potencial per aquest problema: la distància a la recta polar i l'angle amb el pla singular. Primerament es respassaran alguns conceptes, relacionats amb la Grassmanniana de rectes de l'espai, sobre les configuracions singulars dels manipuladors que seran útils per a definir aquests índexos; a continuació es faran quatre simulacions comparant aquests dos nous índexos amb altres dos que es faran servir com a referència. Finalment s'evaluarà la bondat de totes les mesures a partir dels resultats obtinguts a les simulacions.. De manera anàloga com el projectiu dual parametritza els hiperplans, les rectes de l'espai es poden parametritzar mitjançant una varietat anomenada Grassmanniana. Via la immersió de Plücker, aquesta Grassmanniana es pot veure com una hipersuperfície quàdrica dintre d'un espai projectiu de dimensió 5. L'objectiu és estudiar, des del punt de vista algebraic, propietats geomètriques de la Grassmanniana, que ajuden a entendre les configuracions singulars dels robots paral.lels

La principal contribució d'aquest treball és donar les eines i les pautes necessàries per a la linealització per realimentació dels sistemes no holònoms de dues entrades a través del disseny de la forma normal de Goursat. Dissenyarem controladors, de manera que les trajectòries solució passin per unes certes condicions inicials i nals imposades.. Pels braços robòtics tridimensionals a l'espai, i, per tant, no sotmesos a forces externes com la gravetat, les equacions resultants formen un sistema de control no holònom. Si a cada articulació s'hi posa tres motors, els sistema té tres graus de subactuació.A la literatura s'ha dissenyat i controlat sistemes d'auest estil amb dos motors extres a la base a fi que tingui només un grau de subactuació. Es tracta de trobar les condicions a fi que es puguin planificar i fer seguiment de trajectòries en el cas de dos graus de subactuació.

Este trabajo final de máster titulado "Linealización por reglamentación de una clase de manipulador con un número arbitrario de actuadores" estudia las salidas planas para un tipo particular de brazo robótico. El TFM que parte de un trabajo anterior en que se trataron brazos robóticos con 1 y 2 actuadores, amplia los resultados para cualquier número de actuadores. Durante el TFM se estudian en que caso los sistemas son linealizables, ya sea por reglamentación estática o bien por prolongaciones, dando condiciones suficientes y necesarias en cada caso En qualsevol sistema robòtic (i mecànic en general) totalment actuat es pot planificar i/o fer seguiment de trajectòries arbitràries. Tanmateix, si el sistema és sub-actuat, no totes les trajectòries es poden assolir. D'altra banda, la sub-actuació pot ajudar a reduir el cost del robot. La propietat que permet planificar i fer seguiment de trajectòries és la platiutd diferencial. L'objectiu d'aquest projecte és estudiar l'esmentada propietat per a una classe de sistemes robòtics sub-actuats que tenen una específica distribució de la massa. Hi ha resultats coneguts per al cas que el sistema tingui un o dos actuadors. Es tracta, doncs, de generalitzar els resultats a un nombre arbitrari de controls. Les eines que s'utilitzaran en aquest projecte són rudiments d'equacions diferencials i càlculs amb parèntesis de Lie.

Se presentan unas reflexiones sobre el ciclo que las ideas recorren desde que surgen en un entorno universitario hasta que se transforman en un producto industrial. Se concretan estas reflexiones en el contexto de la Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos de la Universitat Politècnica de Catalunya y se presentan algunos ejemplos de éxitos en la implantación del denominado Círculo de las Ideas.

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry., Comment: Final version. Minors changes have been made. 56 pages

Las enfermedades cardiovasculares son la primera causa de muerte de la población Europea. Se estima que la mortalidad por enfermedades cardiovasculares es la mitad de la mortalidad total en toda Europa y provoca 4,35 millones de fallecidos cada año en los 52 estados miembros de la Región Europea. Según la Organización Mundial de la Sanidad (OMS) más de 1,9 millones de muertos en la Unión Europea, además de ser la principal causa de deshabilitad y reducción de calidad de vida. Estos tipos de enfermedades afectan sobre todo a la mayor parte de la población, y, sabiendo que el porcentaje de ancianos en la nuestra sociedad sigue subiendo, se puede fácilmente entender que las cardio-patologías puedan constituir siempre un riesgo elevado para la salud de los países occidentales. La cirugía moderna busca cada día soluciones menos invasivas, como por ejemplo a través de cirugía llamada mini-invasiva. La cirugía mini-invasiva es la técnica quirúrgica que consiente acceder a cavidades internas sin operar incisiones (cirugía en abierto). En esta definición, es trivial intuir que entran sobre todo las técnicas endoscópicas que han permitido realizar muchas operaciones de diferente grado de peligrosidad produciendo numerosos beneficios y reduciendo los índices de riesgo. En la cirugía cardiovascular no es raro encontrar problemáticas de tener que insertar aparatos como stent, válvulas cardiacas, sondas y muchas cosas más a través pequeños orificios (como vasos sanguíneos, por ejemplo, la femoral, la aorta la carótida o la subclavia). Estos aparatos van a ser posicionados o conducidos a través de guías (catéteres) que los conducen hasta el sitio destinado. El hecho de utilizar catéteres que tienen que penetrar por estas vías obliga a que estos aparatos respecten dimensiones muy pequeñas. Es interesante entonces estudiar como estas estructuras deben de soportar esfuerzos de compresión y de expansión cuando vienen insertadas en el catéter y luego se sueltan. El ejemplo en el cual enfocaremos nuestro estudio va a ser un soporte metálico intravascular para cualquier aparato necesite ser anclado en el interior de una vena o arteria.

Let (E;A1;A2;B) be a quadruple of matrices representing a two-order generalized time-invariant linear system, E¨x = A1 ˙ x + A2x + Bu. We study the controllability character under an algebraic point of view.

Let (E;A1;A2;B) be a quadruple of matrices representing a two-order generalized time-invariant linear system, E¨x = A1 ˙ x + A2x + Bu. We study the controllability character under an algebraic point of view.

A natural equivalence relation can be considered in the generalized flag manifold. First we give a complete set of invariants of it as well as a canonical matrix description of the classes. Next we consider parametric flags. We give a miniversal deformation for the above canonical form and we use it to characterize the stable flags.

Given a pair of matrices (A,B) we study the stability of their invariant subspaces from a geometric point of view. The main tool is the manifold of quadruples((A;B); F; S) where S is an (A,B)-invariant subspace and F is such that (A + BF)S C S. From the geometry of this manifold we derive sufficient computable conditions of stability.

Given an orbit space $M/\Gamma$ and an equivalence relation defined in it by means of the action of a group $G$, we obtain a miniversal deformation of an orbit through a miniversal deformation in $M$ with regard to a suitable group action of $G\times \Gamma$. We show some applications to the perturbations of $m$-tuples of subspaces and $(C,A)$-invariant subspaces.

V. I. Arnold constructed smooth generic families of matrices with respect to similarity transformations depending smoothly on the entries of matrices with a small number of parameters. We Solve the same problem for a family of triples of matrices (E; A;B), E;A 2 Mn(C), B 2 Mn£m(C), representing generalized linear systems in the form E ˙ x = Ax+Bu, with respect to feedback and derivative feedback equivalence.

We extend some known results about the smooth stratification of the set of conditioned invariant subspaces for a general pair $(C,A)\in\w C^n\times\w C^{n+m}$ without any assumption on the observability. More precisely we prove that the set of $(C,A)$-conditioned invariant subspaces having a fixed Brunovsky-Kronecker structure is a submanifold of the corresponding Grassman manifold, with a vector bundle structure relating the observable and nonobservable part, and we compute its dimension. We also prove that the set of all $(C,A)$-conditioned invariant subspaces having a fixed dimension is connected, provided that the nonobservable part of $(C,A)$ has at most one eigenvalue (this condition is in general necessary).

Given an orbit space of matrices $M/\Gamma$ and an equivalence relation defined in it by means of the action of a group $G$, we obtain a miniversal deformation of an orbit through a minivesal deformation in $M$ with regard to a suitable group action of $G\times \Gamma$. We show some applications to the perturbations of $m$-tuples of subspaces and $(C,A)$-invariant subspaces.

One of foremost problems in stand-alone photovoltaic systems consists on the election of a strategy for charge controllers. The charge controllers main function is the accumulation system protection, and this leads to an extension of the batteries lifetime, thus reducing, the long term economic cost of the installation. This document describes a Fuzzy Logic based charge controller. In order to show the designed charge controller operation, firstly, a succession of simulations have been carried out to try out the mentioned controller efficiency. Afterwards, the designed charge controller has been used on a real target system to control the charge and discharge processes of a battery in a real stand-alone photovoltaic system, that is installed, on the flat roof of the E.P.S. Jaén of the University of Jaén (Spain). Finally, comparative operation results of the fuzzy charge controller developed are exposed in this document.

El presente artículo presenta un estudio realizado para el Institut d'Estadística de Catalunya, donde se ha aplicado una técnica que trabaja con información subjetiva (el Método Delphi) para obtener unos datos que puedan ser empleados en la alimentación parcial de un modelo matemático, que se nutre principalmente de datos estadísticos (objetivos), con el fin de incrementar la utilidad global del modelo. El artículo justifica la utilización en determinadas circunstancias de la información subjetiva, describe el método Delphi y plantea una serie de proposiciones referentes a la utilidad, empleo y mejora de esta técnica que se ven refrendadas en el caso expuesto.

Fuzzy controllers have been proven to be universal, that is, they can provide any control surface. Their microelectronic implementation is very suitable to achieve high-speed (real-time operation), and low area and power consumption. This paper focuses on discussing the two basic approaches that can be employed to design programmable universal controller integrated circuits. Analog, mixed-signal and digital realizations are summarized and compared.

The ORBEX coprocessor has been designed to execute the typical fuzzy operations of a system based on fuzzy rules. The first real application has been fuzzy controllers for electric cars. The values of the input variables, the position and the orientation of the car with respect the desired trajectory of reference, are obtained from the data provided by a DGPS boarded in the vehicle. The values of the output variables provided by the controller are the angle that the steering wheel has to be turned and the increment of the velocity. Due to the power of the ORBEX coprocessor the controllers can be written with few though meaningful rules., ORBEX Co-processor: CICYT, TIC 96 1393-C06-03. COVAN Project: CAM 06T/042/9.

This work concerns the stability analysis of a non-linear system controlled by a fuzzy T-S control law. It is shown that the closed loop system is in general expressed by a T-S fuzzy system composed of rules with affine linear systems in their consequent parts. The stability of affine T-S systems is then investigated for a special case using as an example the regulation problem of a single link robot arm. Stability conditions are derived using the indirect and direct Lyapunov method and simulation results are presented.

Given an observable system defined by a pair of matrices $(C,A)$ we obtain a cellular decomposition of the manifold of $(C,A)$-conditioned invariant subspaces having the restricted system fixed observability indices and we apply this decomposition to compute their homology groups.

We present an R&D project on fuzzy-logic control applications to the Belgian Nuclear Reactor 1 (BR1) at the Belgian Nuclear Research Centre (SCK•CEN). The project started in 1995 and aimed at investigating the added value of fuzzy logic control for nuclear reactors. We first review some relevant literature on fuzzy logic control in nuclear reactors, then present the state-of-the-art of the BR1 project, with an understanding of the safety requirements for this real fuzzy-logic control application in nuclear reactors.

This paper presents an autonomous vehicle position estimation system based on GPS, that uses a fuzzy sensor fusion technique. A fuzzy path tracking algorithm is also proposed. Both systems have been implemented in the ROMEO-4R vehicle developed at the University of Seville. CICYT project TAP96-1184-C04-01 European Commission ESPRIT LTR 21911

In this paper, a survey of the state of the art and perspectives of two main lines of research in fuzzy control systems is presented: on one hand, the \emph{interpolative-functional line} representing fuzzy systems as parameterized universal function approximators, thus applying nonlinear control and neural network paradigms; on the other hand, a \emph{logic-formal} approach where fuzzy systems are analysed in terms of logic interpretations, exploring validation, consistency and completeness, uncertainty management and knowledge supervision. The former approach is not widely used in the control field, and asserting its possibilities is one of the main motivations of this paper. References in both lines and some abridged results in the second case are cited, in particular some of the author's contributions, to which the interested reader is referred.

Analog circuits provide better area/power efficiency than their digital counterparts for low-medium precision requirements [1]. This limit in precision, as well as the lack of design tools when compared to the digital approach, imposes a limit of complexity, hence fuzzy analog controllers are usually oriented to fast low-power systems with low-medium complexity. This paper presents a strategy to preserve most of the advantages of an analog implementation, while allowing a notorious increment of the system complexity. Such strategy consists in implementing a reduced number of rules, those that really determine the output in a lattice controller, which we call analog core, then this core is dynamically programmed to perform the computation related to a specific rule set. The data to program the analog core are stored in a memory, and constitutes the whole knowledge base in a kind of virtual rule set. An example 64-rule, 2-input, 4-bit singleton controller has been designed in a CMOS 0.7$\mu$mm technology to demonstrate the viability of the architecture. The measured input-output delay is around 500ns for a power consumption of 16mW and a chip area (without pads) of 2.65mm$^2$.

This paper focus on the problem of decomposing multivariable fuzzy controllers using a hierarchical approach based on the application of meta-knowledge. Usually, hierarchical fuzzy systems are based on a cascade structure of fuzzy logic controllers where the output of each level is considered as one of the inputs to the following level. The paper introduces a different approach, to the idea of hierarchy, where the output of a level is considered not as input to the following level controller but as a semantics modifier.

This paper describes the design and development of a sensor based navigation system which makes it possible for a non-holonomous mobile robot to avoid obstacles using information on its environment picked up by a belt of ultrasonic sensors. To control the robot no preliminary information regarding its environment is required, the robot adapts to them through the information gathered on the spot by the ultrasonic sensors and the information released from a spatial memory. The controller, which allows the generation of the signal to the robot's motors, has been developed based on the concept of general perception, and the principles of fuzzy logic have been applied. The platform on which the navigation system has been tested, is a prototype mobile robot (VEA-II) developed at IKERLAN, which is highly manoeuvrable, and capable of moving both in a holonomous and non-holonomous configurations.

This paper deals with the decomposition problem of a multivariable fuzzy controller. For this, is proposed the use of notions taken from the framework of the Game Theory. Using the notion of {\it couple} between variables, a partition of the rule space in subsystems is obtained. The subsystems are considered players that corrects the actions of the others. These ideas are applied to the control of a polymerization reactor (CSTR).

We discuss a prescriptive approach to multistage optimal fuzzy control of a fuzzy system, given by a fuzzy state transition equation. Fuzzy constraints and fuzzy goals at consecutive control stages are given, and their confluence, Bellman and Zadeh's fuzzy decision, is an explicit performance function to be optimized. First, we briefly survey previous basic solution methods of dynamic programming (Baldwin and Pilsworth, 1982) and branch-and-bound (Kacprzyk, 1979), which are plagued by low numerical efficiency, and then sketch Kacprzyk's (1993a--e, 1994a) approach based on possibilistic interpolative reasoning aimed at enhancing the numerical efficiency but requiring a solution of a simplified auxiliary problem, and then some "readjustment" of the solution obtained. We propose a genetic algorithm for solving the problem considered. Real coding and specially defined operations of crossover, mutation, etc. are employed. The approach yields good results, and is quite efficient numerically

Description of individuals in ill-structured domains produces messy data matrices. In this context, automated classification requires the management of those kind of matrices. One of the features involved in clustering is the evaluation of distances between individuals. Then, a special function to calculate distances between individuals partially simultaneously described by qualitative and quantitative variables is required. In this paper properties and details of the metrics used by Klass in this situation is presented --- Klass is a clustering system oriented to the classification of ill-structured domains which implements an adapted version of the reciprocal neighbors algorithm; it also takes advantage of any additional information that an expert can provide about the target concepts.

Fuzzy controllers are able to incorporate knowledge expressed in if-then rules. These rules are given by experts or skilful operators. Problems arise when there are not experts or/and rules are not easy to find. Authors' proposal consists in an analog fuzzy controller which accepts structured language as well as input/output data pairs, thus rules can be extracted or tuned from human or software controller operation. Learning from data pairs has to be carried out under hardware restrictions in linearity, range and resolution. In this paper, modelling of building blocks arranged in a neuro-fuzzy architecture is made and issues related to on-chip learning are discussed. Computer simulations show that learning is possible for resolutions up to 6 bits, affordable with the cheapest VLSI technologies.

This paper describes a design environment for the hardware realizations of fuzzy controllers which includes a set of CAD tools to ease the description, verification and synthesis of this kind of systems. Special emphasis is focused on the use of a standard hardware description language (VHDL) and compatibility with other integrated circuits design tools.

We find explicit miniversal deformations of flags in the generalized flag manifolds, with regard a natural equivalence relation defined by the group action that keeps fixed the reference flag.

We consider the topology of the set of conditioned invariant subspaces of an observable pair $(C,A)$ of a fixed dimension. By fixing the observability indices of the restricted system, a stratification by finitely many smooth manifolds is obtained, termed Brunovsky strata. It is shown that each Brunovsky stratum is homotopy equivalent to a generalized flag manifold. From this description an effective formula for the Betti numbers of the Brunovsky strata can be derived.

Proper Generalized Decomposition (PGD) is devised as a computational method to solve high-dimensionalboundary value problems(where many dimensions are associated with the space of parameters defining the problem). The PGD philosophy consists in providing a separated representation of the multidimensional solution using agreedy approachcombined with an alternated directions scheme to obtain the successive rank-one terms. This paper presents an algorithmic approach to high-dimensional tensorseparation based on solving theLeast Squares approximationin a separable format of multidimensional tensor using PGD. This strategy is usually embedded in a standard PGD code in order to compress the solution (reduce the number of terms and optimize the available storage capacity), but it stands also as an alternative and highly competitive method for tensor separation.

This work presents a new technique to securely transmit and retrieve a message signal via chaotic systems. In our system, a two-valued message signal modulates the frequency of a Duffing oscillator sinusoidal term. An observer is used in the receiver side to retrieve the sinusoidal signal that contains the message and a novel frequency estimator is then used to reproduce an approximated estimation of the message signal. The performance of the system is analyzed by means of numerical simulations performed in Matlab.

Probe-based technologies are proliferating as a means of inferring traffic states. Technological companies are interested in traffic data for computing the best routes in a traffic-aware manner and they also provide real-time traffic information with certain temporal accuracy. This paper analyses and evaluates how data provided by a fleet of probe cars can be used to develop a navigation service and how the penetration rate of this service affects a set of city-scale KPIs (Key Performance Indicators) and driver KPIs. The case study adopts a model-driven approach in which microscopic simulation emulates real-size fleets of probe vehicles that provide positions and speed data. What is noteworthy about the modelling behaviour is that drivers are segmented according to their knowledge of network conditions for selected trips: experts, regular drivers, and tourists. The paper presents and discusses the modelling approach and the results obtained from an experimental Barcelona CBD model designed to evaluate the penetration rates of probe vehicles and route guidance. An analysis of the simulation experiments reveals remarkable links among city-scale KPIs, which—from a multivariate point of view—is a novelty. A simulation-based framework for results analysis and visualization is also introduced in order to simplify the simulation results analysis and easily visualize OD paths for driver segments. Throughout this work, the authors have benefited from the support of inLab FIB team at UPC and the suggestions of Jaume Barceló (Emeritus Professor at UPC). This research was funded by Spanish R+D Programs, TRA2016-76914-C3-1-P, and by Secretaria d’Universitats-i-Recerca-Generalitat de Catalunya, 2017-SGR-1749.

This paper proposes a fault detection method for hysteretic base-isolation systems. One of the key contributions of this work is a Lyapunov-based restoring force observer that leads to the design of a robust fault detection scheme. The different fault types considered are stiffness and damping variations in the system. The proposed fault estimation method provides a direct estimate of the size and severity of the fault, which can be important in many civil engineering applications. A design procedure is described, and nonlinear simulation results are presented to demonstrate the applicability of the proposed method.

New sustainable mobility concepts and smart resilient ideas are arising every day. However, there is not an easy way to bring these ideas into reality, or to test how good they are as mobility solutions. Virtual Mobility Lab offers the opportunity to evaluate the impact of new mobility concepts before taking them to the real world. In this work, a multimodal macroscopic traffic simulation model of the Barcelona Metropolitan Area is developed, including both public and private transport network. This paper explains the remarkable features developed for this model, such as the network hierarchy and the multimodal public network interchangers, allowing demand to exchange between public transportation modes along their origin-destination paths.

Given an observable system (C,A)€ K^(mxn)X K^(nxn)with K=R or C, the set of (C,A)-invariant subspaces having the restricted system fixed observability indices is a smooth manifold embedded on the corresponding Grassmannian. We obtain an explicit parametrization of it by means of an atlas of corresponding charts. As an application we obtain the set of maximal dimensional outputs making solvable a generic Disturbance Decoupling Problem.