Resilience analysis of networked systems-of-systems based on structural and dynamic interdependencies

Critical infrastructures support everyday activities in modern societies, facilitating the exchange of services and quantities of various nature. Their functioning is the result of the integration of diverse technologies, systems and organizations into a complex network of interconnections. Benefits from networking are accompanied by new threats and risks. In particular, because of the increased interdependency, disturbances and failures may propagate and render unstable the whole infrastructure network. This paper presents a methodology of resilience analysis of networked systems of systems. Resilience generalizes the concept of stability of a system around a state of equilibrium, with respect to a disturbance and its ability of preventing, resisting and recovery. The methodology provides a tool for the analysis of off-equilibrium conditions that may occur in a single system and propagate through the network of dependencies. The analysis is conducted in two stages. The first stage of the analysis is qualitative. It identifies the resilience scenarios, i.e. the sequence of events, triggered by an initial disturbance, which include failures and the system response. The second stage is quantitative. The most critical scenarios can be simulated, for the desired parameter settings, in order to check if they are successfully handled, i.e recovered to nominal conditions, or they end into the network failure. The proposed methodology aims at providing an effective support to resilience-informed design.

Mining recurring concepts in a dynamic feature space

Most data stream classification techniques assume that the underlying feature space is static. However, in real-world applications the set of features and their relevance to the target concept may change over time. In addition, when the underlying concepts reappear, reusing previously learnt models can enhance the learning process in terms of accuracy and processing time at the expense of manageable memory consumption. In this paper, we propose mining recurring concepts in a dynamic feature space (MReC-DFS), a data stream classification system to address the challenges of learning recurring concepts in a dynamic feature space while simultaneously reducing the memory cost associated with storing past models. MReC-DFS is able to detect and adapt to concept changes using the performance of the learning process and contextual information. To handle recurring concepts, stored models are combined in a dynamically weighted ensemble. Incremental feature selection is performed to reduce the combined feature space. This contribution allows MReC-DFS to store only the features most relevant to the learnt concepts, which in turn increases the memory efficiency of the technique. In addition, an incremental feature selection method is proposed that dynamically determines the threshold between relevant and irrelevant features. Experimental results demonstrating the high accuracy of MReC-DFS compared with state-of-the-art techniques on a variety of real datasets are presented. The results also show the superior memory efficiency of MReC-DFS.

Collective Organization of Complex Networks: Emergent Scales, Vulnerability, and Targeting of Desired Dynamics

Cuando una colectividad de sistemas dinámicos acoplados mediante una estructura irregular de interacciones evoluciona, se observan dinámicas de gran complejidad y fenómenos emergentes imposibles de predecir a partir de las propiedades de los sistemas individuales. El objetivo principal de esta tesis es precisamente avanzar en nuestra comprensión de la relación existente entre la topología de interacciones y las dinámicas colectivas que una red compleja es capaz de mantener. Siendo este un tema amplio que se puede abordar desde distintos puntos de vista, en esta tesis se han estudiado tres problemas importantes dentro del mismo que están relacionados entre sí. Por un lado, en numerosos sistemas naturales y artificiales que se pueden describir mediante una red compleja la topología no es estática, sino que depende de la dinámica que se desarrolla en la red: un ejemplo son las redes de neuronas del cerebro. En estas redes adaptativas la propia topología emerge como consecuencia de una autoorganización del sistema. Para conocer mejor cómo pueden emerger espontáneamente las propiedades comúnmente observadas en redes reales, hemos estudiado el comportamiento de sistemas que evolucionan según reglas adaptativas locales con base empírica. Nuestros resultados numéricos y analíticos muestran que la autoorganización del sistema da lugar a dos de las propiedades más universales de las redes complejas: a escala mesoscópica, la aparición de una estructura de comunidades, y, a escala macroscópica, la existencia de una ley de potencias en la distribución de las interacciones en la red. El hecho de que estas propiedades aparecen en dos modelos con leyes de evolución cuantitativamente distintas que siguen unos mismos principios adaptativos sugiere que estamos ante un fenómeno que puede ser muy general, y estar en el origen de estas propiedades en sistemas reales. En segundo lugar, proponemos una medida que permite clasificar los elementos de una red compleja en función de su relevancia para el mantenimiento de dinámicas colectivas. En concreto, estudiamos la vulnerabilidad de los distintos elementos de una red frente a perturbaciones o grandes fluctuaciones, entendida como una medida del impacto que estos acontecimientos externos tienen en la interrupción de una dinámica colectiva. Los resultados que se obtienen indican que la vulnerabilidad dinámica es sobre todo dependiente de propiedades locales, por tanto nuestras conclusiones abarcan diferentes topologías, y muestran la existencia de una dependencia no trivial entre la vulnerabilidad y la conectividad de los elementos de una red. Finalmente, proponemos una estrategia de imposición de una dinámica objetivo genérica en una red dada e investigamos su validez en redes con diversas topologías que mantienen regímenes dinámicos turbulentos. Se obtiene como resultado que las redes heterogéneas (y la amplia mayora de las redes reales estudiadas lo son) son las más adecuadas para nuestra estrategia de targeting de dinámicas deseadas, siendo la estrategia muy efectiva incluso en caso de disponer de un conocimiento muy imperfecto de la topología de la red. Aparte de la relevancia teórica para la comprensión de fenómenos colectivos en sistemas complejos, los métodos y resultados propuestos podrán dar lugar a aplicaciones en sistemas experimentales y tecnológicos, como por ejemplo los sistemas neuronales in vitro, el sistema nervioso central (en el estudio de actividades síncronas de carácter patológico), las redes eléctricas o los sistemas de comunicaciones. ABSTRACT The time evolution of an ensemble of dynamical systems coupled through an irregular interaction scheme gives rise to dynamics of great of complexity and emergent phenomena that cannot be predicted from the properties of the individual systems. The main objective of this thesis is precisely to increase our understanding of the interplay between the interaction topology and the collective dynamics that a complex network can support. This is a very broad subject, so in this thesis we will limit ourselves to the study of three relevant problems that have strong connections among them. First, it is a well-known fact that in many natural and manmade systems that can be represented as complex networks the topology is not static; rather, it depends on the dynamics taking place on the network (as it happens, for instance, in the neuronal networks in the brain). In these adaptive networks the topology itself emerges from the self-organization in the system. To better understand how the properties that are commonly observed in real networks spontaneously emerge, we have studied the behavior of systems that evolve according to local adaptive rules that are empirically motivated. Our numerical and analytical results show that self-organization brings about two of the most universally found properties in complex networks: at the mesoscopic scale, the appearance of a community structure, and, at the macroscopic scale, the existence of a power law in the weight distribution of the network interactions. The fact that these properties show up in two models with quantitatively different mechanisms that follow the same general adaptive principles suggests that our results may be generalized to other systems as well, and they may be behind the origin of these properties in some real systems. We also propose a new measure that provides a ranking of the elements in a network in terms of their relevance for the maintenance of collective dynamics. Specifically, we study the vulnerability of the elements under perturbations or large fluctuations, interpreted as a measure of the impact these external events have on the disruption of collective motion. Our results suggest that the dynamic vulnerability measure depends largely on local properties (our conclusions thus being valid for different topologies) and they show a non-trivial dependence of the vulnerability on the connectivity of the network elements. Finally, we propose a strategy for the imposition of generic goal dynamics on a given network, and we explore its performance in networks with different topologies that support turbulent dynamical regimes. It turns out that heterogeneous networks (and most real networks that have been studied belong in this category) are the most suitable for our strategy for the targeting of desired dynamics, the strategy being very effective even when the knowledge on the network topology is far from accurate. Aside from their theoretical relevance for the understanding of collective phenomena in complex systems, the methods and results here discussed might lead to applications in experimental and technological systems, such as in vitro neuronal systems, the central nervous system (where pathological synchronous activity sometimes occurs), communication systems or power grids.

Gear dynamics monitoring using discrete wavelet transformation and multi-layer perceptron neural networks

This paper presents a multi-stage algorithm for the dynamic condition monitoring of a gear. The algorithm provides information referred to the gear status (fault or normal condition) and estimates the mesh stiffness per shaft revolution in case that any abnormality is detected. In the first stage, the analysis of coefficients generated through discrete wavelet transformation (DWT) is proposed as a fault detection and localization tool. The second stage consists in establishing the mesh stiffness reduction associated with local failures by applying a supervised learning mode and coupled with analytical models. To do this, a multi-layer perceptron neural network has been configured using as input features statistical parameters sensitive to torsional stiffness decrease and derived from wavelet transforms of the response signal. The proposed method is applied to the gear condition monitoring and results show that it can update the mesh dynamic properties of the gear on line.

Modelling uncertainty of flood quantile estimation at ungauged sites by Bayesian networks

Prediction at ungauged sites is essential for water resources planning and management. Ungauged sites have no observations about the magnitude of floods, but some site and basin characteristics are known. Regression models relate physiographic and climatic basin characteristics to flood quantiles, which can be estimated from observed data at gauged sites. However, these models assume linear relationships between variables Prediction intervals are estimated by the variance of the residuals in the estimated model. Furthermore, the effect of the uncertainties in the explanatory variables on the dependent variable cannot be assessed. This paper presents a methodology to propagate the uncertainties that arise in the process of predicting flood quantiles at ungauged basins by a regression model. In addition, Bayesian networks were explored as a feasible tool for predicting flood quantiles at ungauged sites. Bayesian networks benefit from taking into account uncertainties thanks to their probabilistic nature. They are able to capture non-linear relationships between variables and they give a probability distribution of discharges as result. The methodology was applied to a case study in the Tagus basin in Spain.

Disparate connectivity for structural and functional networks is revealed when physical location of the connected nodes is considered

Macroscopic brain networks have been widely described with the manifold of metrics available using graph theory. However, most analyses do not incorporate information about the physical position of network nodes. Here, we provide a multimodal macroscopic network characterization while considering the physical positions of nodes. To do so, we examined anatomical and functional macroscopic brain networks in a sample of twenty healthy subjects. Anatomical networks are obtained with a graph based tractography algorithm from diffusion-weighted magnetic resonance images (DW-MRI). Anatomical con- nections identified via DW-MRI provided probabilistic constraints for determining the connectedness of 90 dif- ferent brain areas. Functional networks are derived from temporal linear correlations between blood-oxygenation level-dependent signals derived from the same brain areas. Rentian Scaling analysis, a technique adapted from very- large-scale integration circuits analyses, shows that func- tional networks are more random and less optimized than the anatomical networks. We also provide a new metric that allows quantifying the global connectivity arrange- ments for both structural and functional networks. While the functional networks show a higher contribution of inter-hemispheric connections, the anatomical networks highest connections are identified in a dorsal?ventral arrangement. These results indicate that anatomical and functional networks present different connectivity organi- zations that can only be identified when the physical locations of the nodes are included in the analysis.

Learning Bayesian networks from data by the incremental compilation of new network polynomials

Probabilistic graphical models are a huge research field in artificial intelligence nowadays. The scope of this work is the study of directed graphical models for the representation of discrete distributions. Two of the main research topics related to this area focus on performing inference over graphical models and on learning graphical models from data. Traditionally, the inference process and the learning process have been treated separately, but given that the learned models structure marks the inference complexity, this kind of strategies will sometimes produce very inefficient models. With the purpose of learning thinner models, in this master thesis we propose a new model for the representation of network polynomials, which we call polynomial trees. Polynomial trees are a complementary representation for Bayesian networks that allows an efficient evaluation of the inference complexity and provides a framework for exact inference. We also propose a set of methods for the incremental compilation of polynomial trees and an algorithm for learning polynomial trees from data using a greedy score+search method that includes the inference complexity as a penalization in the scoring function.

Expressive power of binary relevance and chain classifiers based on Bayesian Networks for multi-label classification

Bayesian network classifiers are widely used in machine learning because they intuitively represent causal relations. Multi-label classification problems require each instance to be assigned a subset of a defined set of h labels. This problem is equivalent to finding a multi-valued decision function that predicts a vector of h binary classes. In this paper we obtain the decision boundaries of two widely used Bayesian network approaches for building multi-label classifiers: Multi-label Bayesian network classifiers built using the binary relevance method and Bayesian network chain classifiers. We extend our previous single-label results to multi-label chain classifiers, and we prove that, as expected, chain classifiers provide a more expressive model than the binary relevance method.

Cognitive test-bed for wireless sensor networks

Cognitive Wireless Sensor Networks are an emerging technology with a vast potential to avoid traditional wireless problems such as reliability, interferences and spectrum scarcity in Wireless Sensor Networks. Cognitive Wireless Sensor Networks test-beds are an important tool for future developments, protocol strategy testing and algorithm optimization in real scenarios. A new cognitive test-bed for Cognitive Wireless Sensor Networks is presented in this paper. This work in progress includes both the design of a cognitive simulator for networks with a high number of nodes and the implementation of a new platform with three wireless interfaces and a cognitive software for extracting real data. Finally, as a future work, a remote programmable system and the planning for the physical deployment of the nodes at the university building is presented.

The Balanced Cross-Layer Design Routing Algorithm in Wireless Sensor Networks Using Fuzzy Logic

Recently, the cross-layer design for the wireless sensor network communication protocol has become more and more important and popular. Considering the disadvantages of the traditional cross-layer routing algorithms, in this paper we propose a new fuzzy logic-based routing algorithm, named the Balanced Cross-layer Fuzzy Logic (BCFL) routing algorithm. In BCFL, we use the cross-layer parameters’ dispersion as the fuzzy logic inference system inputs. Moreover, we give each cross-layer parameter a dynamic weight according the value of the dispersion. For getting a balanced solution, the parameter whose dispersion is large will have small weight, and vice versa. In order to compare it with the traditional cross-layer routing algorithms, BCFL is evaluated through extensive simulations. The simulation results show that the new routing algorithm can handle the multiple constraints without increasing the complexity of the algorithm and can achieve the most balanced performance on selecting the next hop relay node. Moreover, the Balanced Cross-layer Fuzzy Logic routing algorithm can adapt to the dynamic changing of the network conditions and topology effectively.

Nepfix: on-demand cloud elastic simulation of networks of evolutionary processors

Una Red de Procesadores Evolutivos o NEP (por sus siglas en ingles), es un modelo computacional inspirado por el modelo evolutivo de las celulas, específicamente por las reglas de multiplicación de las mismas. Esta inspiración hace que el modelo sea una abstracción sintactica de la manipulation de information de las celulas. En particu¬lar, una NEP define una maquina de cómputo teorica capaz de resolver problemas NP completos de manera eficiente en tóerminos de tiempo. En la praóctica, se espera que las NEP simuladas en móaquinas computacionales convencionales puedan resolver prob¬lemas reales complejos (que requieran ser altamente escalables) a cambio de una alta complejidad espacial. En el modelo NEP, las cóelulas estóan representadas por palabras que codifican sus secuencias de ADN. Informalmente, en cualquier momento de cómputo del sistema, su estado evolutivo se describe como un coleccion de palabras, donde cada una de ellas representa una celula. Estos momentos fijos de evolucion se denominan configuraciones. De manera similar al modelo biologico, las palabras (celulas) mutan y se dividen en base a bio-operaciones sencillas, pero solo aquellas palabras aptas (como ocurre de forma parecida en proceso de selection natural) seran conservadas para la siguiente configuracióon. Una NEP como herramienta de computation, define una arquitectura paralela y distribuida de procesamiento simbolico, en otras palabras, una red de procesadores de lenguajes. Desde el momento en que el modelo fue propuesto a la comunidad científica en el año 2001, múltiples variantes se han desarrollado y sus propiedades respecto a la completitud computacional, eficiencia y universalidad han sido ampliamente estudiadas y demostradas. En la actualidad, por tanto, podemos considerar que el modelo teórico NEP se encuentra en el estadio de la madurez. La motivación principal de este Proyecto de Fin de Grado, es proponer una aproxi-mación práctica que permita dar un salto del modelo teórico NEP a una implantación real que permita su ejecucion en plataformas computacionales de alto rendimiento, con el fin de solucionar problemas complejos que demanda la sociedad actual. Hasta el momento, las herramientas desarrolladas para la simulation del modelo NEP, si bien correctas y con resultados satisfactorios, normalmente estón atadas a su entorno de ejecucion, ya sea el uso de hardware específico o implementaciones particulares de un problema. En este contexto, el propósito fundamental de este trabajo es el desarrollo de Nepfix, una herramienta generica y extensible para la ejecucion de cualquier algo¬ritmo de un modelo NEP (o alguna de sus variantes), ya sea de forma local, como una aplicación tradicional, o distribuida utilizando los servicios de la nube. Nepfix es una aplicacion software desarrollada durante 7 meses y que actualmente se encuentra en su segunda iteration, una vez abandonada la fase de prototipo. Nepfix ha sido disenada como una aplicacion modular escrita en Java 8 y autocontenida, es decir, no requiere de un entorno de ejecucion específico (cualquier maquina virtual de Java es un contenedor vólido). Nepfix contiene dos componentes o móodulos. El primer móodulo corresponde a la ejecución de una NEP y es por lo tanto, el simulador. Para su desarrollo, se ha tenido en cuenta el estado actual del modelo, es decir, las definiciones de los procesadores y filtros mas comunes que conforman la familia del modelo NEP. Adicionalmente, este componente ofrece flexibilidad en la ejecucion, pudiendo ampliar las capacidades del simulador sin modificar Nepfix, usando para ello un lenguaje de scripting. Dentro del desarrollo de este componente, tambióen se ha definido un estóandar de representacióon del modelo NEP basado en el formato JSON y se propone una forma de representation y codificación de las palabras, necesaria para la comunicación entre servidores. Adicional-mente, una característica importante de este componente, es que se puede considerar una aplicacion aislada y por tanto, la estrategia de distribution y ejecución son total-mente independientes. El segundo moódulo, corresponde a la distribucióon de Nepfix en la nube. Este de-sarrollo es el resultado de un proceso de i+D, que tiene una componente científica considerable. Vale la pena resaltar el desarrollo de este modulo no solo por los resul-tados prócticos esperados, sino por el proceso de investigation que se se debe abordar con esta nueva perspectiva para la ejecución de sistemas de computación natural. La principal característica de las aplicaciones que se ejecutan en la nube es que son gestionadas por la plataforma y normalmente se encapsulan en un contenedor. En el caso de Nepfix, este contenedor es una aplicacion Spring que utiliza el protocolo HTTP o AMQP para comunicarse con el resto de instancias. Como valor añadido, Nepfix aborda dos perspectivas de implementation distintas (que han sido desarrolladas en dos iteraciones diferentes) del modelo de distribution y ejecucion, que tienen un impacto muy significativo en las capacidades y restricciones del simulador. En concreto, la primera iteration utiliza un modelo de ejecucion asincrono. En esta perspectiva asincrona, los componentes de la red NEP (procesadores y filtros) son considerados como elementos reactivos a la necesidad de procesar una palabra. Esta implementation es una optimization de una topologia comun en el modelo NEP que permite utilizar herramientas de la nube para lograr un escalado transparente (en lo ref¬erente al balance de carga entre procesadores) pero produce efectos no deseados como indeterminacion en el orden de los resultados o imposibilidad de distribuir eficiente-mente redes fuertemente interconectadas. Por otro lado, la segunda iteration corresponde al modelo de ejecucion sincrono. Los elementos de una red NEP siguen un ciclo inicio-computo-sincronizacion hasta que el problema se ha resuelto. Esta perspectiva sincrona representa fielmente al modelo teórico NEP pero el proceso de sincronizacion es costoso y requiere de infraestructura adicional. En concreto, se requiere un servidor de colas de mensajes RabbitMQ. Sin embargo, en esta perspectiva los beneficios para problemas suficientemente grandes superan a los inconvenientes, ya que la distribuciín es inmediata (no hay restricciones), aunque el proceso de escalado no es trivial. En definitiva, el concepto de Nepfix como marco computacional se puede considerar satisfactorio: la tecnología es viable y los primeros resultados confirman que las carac-terísticas que se buscaban originalmente se han conseguido. Muchos frentes quedan abiertos para futuras investigaciones. En este documento se proponen algunas aproxi-maciones a la solucion de los problemas identificados como la recuperacion de errores y la division dinamica de una NEP en diferentes subdominios. Por otra parte, otros prob-lemas, lejos del alcance de este proyecto, quedan abiertos a un futuro desarrollo como por ejemplo, la estandarización de la representación de las palabras y optimizaciones en la ejecucion del modelo síncrono. Finalmente, algunos resultados preliminares de este Proyecto de Fin de Grado han sido presentados recientemente en formato de artículo científico en la "International Work-Conference on Artificial Neural Networks (IWANN)-2015" y publicados en "Ad-vances in Computational Intelligence" volumen 9094 de "Lecture Notes in Computer Science" de Springer International Publishing. Lo anterior, es una confirmation de que este trabajo mas que un Proyecto de Fin de Grado, es solo el inicio de un trabajo que puede tener mayor repercusion en la comunidad científica. Abstract Network of Evolutionary Processors -NEP is a computational model inspired by the evolution of cell populations, which might model some properties of evolving cell communities at the syntactical level. NEP defines theoretical computing devices able to solve NP complete problems in an efficient manner. In this model, cells are represented by words which encode their DNA sequences. Informally, at any moment of time, the evolutionary system is described by a collection of words, where each word represents one cell. Cells belong to species and their community evolves according to mutations and division which are defined by operations on words. Only those cells are accepted as surviving (correct) ones which are represented by a word in a given set of words, called the genotype space of the species. This feature is analogous with the natural process of evolution. Formally, NEP is based on an architecture for parallel and distributed processing, in other words, a network of language processors. Since the date when NEP was pro¬posed, several extensions and variants have appeared engendering a new set of models named Networks of Bio-inspired Processors (NBP). During this time, several works have proved the computational power of NBP. Specifically, their efficiency, universality, and computational completeness have been thoroughly investigated. Therefore, we can say that the NEP model has reached its maturity. The main motivation for this End of Grade project (EOG project in short) is to propose a practical approximation that allows to close the gap between theoretical NEP model and a practical implementation in high performing computational platforms in order to solve some of high the high complexity problems society requires today. Up until now tools developed to simulate NEPs, while correct and successful, are usu¬ally tightly coupled to the execution environment, using specific software frameworks (Hadoop) or direct hardware usage (GPUs). Within this context the main purpose of this work is the development of Nepfix, a generic and extensible tool that aims to execute algorithms based on NEP model and compatible variants in a local way, similar to a traditional application or in a distributed cloud environment. Nepfix as an application was developed during a 7 month cycle and is undergoing its second iteration once the prototype period was abandoned. Nepfix is designed as a modular self-contained application written in Java 8, that is, no additional external dependencies are required and it does not rely on an specific execution environment, any JVM is a valid container. Nepfix is made of two components or modules. The first module corresponds to the NEP execution and therefore simulation. During the development the current state of the theoretical model was used as a reference including most common filters and processors. Additionally extensibility is provided by the use of Python as a scripting language to run custom logic. Along with the simulation a definition language for NEP has been defined based on JSON as well as a mechanisms to represent words and their possible manipulations. NEP simulator is isolated from distribution and as mentioned before different applications that include it as a dependency are possible, the distribution of NEPs is an example of this. The second module corresponds to executing Nepfix in the cloud. The development carried a heavy R&D process since this front was not explored by other research groups until now. It's important to point out that the development of this module is not focused on results at this point in time, instead we focus on feasibility and discovery of this new perspective to execute natural computing systems and NEPs specifically. The main properties of cloud applications is that they are managed by the platform and are encapsulated in a container. For Nepfix a Spring application becomes the container and the HTTP or AMQP protocols are used for communication with the rest of the instances. Different execution perspectives were studied, namely asynchronous and synchronous models were developed for solving different kind of problems using NEPs. Different limitations and restrictions manifest in both models and are explored in detail in the respective chapters. In conclusion we can consider that Nepfix as a computational framework is suc-cessful: Cloud technology is ready for the challenge and the first results reassure that the properties Nepfix project pursued were met. Many investigation branches are left open for future investigations. In this EOG implementation guidelines are proposed for some of them like error recovery or dynamic NEP splitting. On the other hand other interesting problems that were not in the scope of this project were identified during development like word representation standardization or NEP model optimizations. As a confirmation that the results of this work can be useful to the scientific com-munity a preliminary version of this project was published in The International Work- Conference on Artificial Neural Networks (IWANN) in May 2015. Development has not stopped since that point and while Nepfix in it's current state can not be consid¬ered a final product the most relevant ideas, possible problems and solutions that were produced during the seven months development cycle are worthy to be gathered and presented giving a meaning to this EOG work.

Development of a fuzzy control based self-adaptive system for energy saving in constrained networks for the Internet of Things

Las redes del futuro, incluyendo las redes de próxima generación, tienen entre sus objetivos de diseño el control sobre el consumo de energía y la conectividad de la red. Estos objetivos cobran especial relevancia cuando hablamos de redes con capacidades limitadas, como es el caso de las redes de sensores inalámbricos (WSN por sus siglas en inglés). Estas redes se caracterizan por estar formadas por dispositivos de baja o muy baja capacidad de proceso y por depender de baterías para su alimentación. Por tanto la optimización de la energía consumida se hace muy importante. Son muchas las propuestas que se han realizado para optimizar el consumo de energía en este tipo de redes. Quizás las más conocidas son las que se basan en la planificación coordinada de periodos de actividad e inactividad, siendo una de las formas más eficaces para extender el tiempo de vida de las baterías. La propuesta que se presenta en este trabajo se basa en el control de la conectividad mediante una aproximación probabilística. La idea subyacente es que se puede esperar que una red mantenga la conectividad si todos sus nodos tienen al menos un número determinado de vecinos. Empleando algún mecanismo que mantenga ese número, se espera que se pueda mantener la conectividad con un consumo energético menor que si se empleara una potencia de transmisión fija que garantizara una conectividad similar. Para que el mecanismo sea eficiente debe tener la menor huella posible en los dispositivos donde se vaya a emplear. Por eso se propone el uso de un sistema auto-adaptativo basado en control mediante lógica borrosa. En este trabajo se ha diseñado e implementado el sistema descrito, y se ha probado en un despliegue real confirmando que efectivamente existen configuraciones posibles que permiten mantener la conectividad ahorrando energía con respecto al uso de una potencia de transmisión fija. ABSTRACT. Among the design goals for future networks, including next generation networks, we can find the energy consumption and the connectivity. These two goals are of special relevance when dealing with constrained networks. That is the case of Wireless Sensors Networks (WSN). These networks consist of devices with low or very low processing capabilities. They also depend on batteries for their operation. Thus energy optimization becomes a very important issue. Several proposals have been made for optimizing the energy consumption in this kind of networks. Perhaps the best known are those based on the coordinated planning of active and sleep intervals. They are indeed one of the most effective ways to extend the lifetime of the batteries. The proposal presented in this work uses a probabilistic approach to control the connectivity of a network. The underlying idea is that it is highly probable that the network will have a good connectivity if all the nodes have a minimum number of neighbors. By using some mechanism to reach that number, we hope that we can preserve the connectivity with a lower energy consumption compared to the required one if a fixed transmission power is used to achieve a similar connectivity. The mechanism must have the smallest footprint possible on the devices being used in order to be efficient. Therefore a fuzzy control based self-adaptive system is proposed. This work includes the design and implementation of the described system. It also has been validated in a real scenario deployment. We have obtained results supporting that there exist configurations where it is possible to get a good connectivity saving energy when compared to the use of a fixed transmission power for a similar connectivity.