A study on the performance of flexible pavements on mature soil subgrades

The country has witnessed tremendous increase in the vehicle population and increased axle loading pattern during the last decade, leaving its road network overstressed and leading to premature failure. The type of deterioration present in the pavement should be considered for determining whether it has a functional or structural deficiency, so that appropriate overlay type and design can be developed. Structural failure arises from the conditions that adversely affect the load carrying capability of the pavement structure. Inadequate thickness, cracking, distortion and disintegration cause structural deficiency. Functional deficiency arises when the pavement does not provide a smooth riding surface and comfort to the user. This can be due to poor surface friction and texture, hydro planning and splash from wheel path, rutting and excess surface distortion such as potholes, corrugation, faulting, blow up, settlement, heaves etc. Functional condition determines the level of service provided by the facility to its users at a particular time and also the Vehicle Operating Costs (VOC), thus influencing the national economy. Prediction of the pavement deterioration is helpful to assess the remaining effective service life (RSL) of the pavement structure on the basis of reduction in performance levels, and apply various alternative designs and rehabilitation strategies with a long range funding requirement for pavement preservation. In addition, they can predict the impact of treatment on the condition of the sections. The infrastructure prediction models can thus be classified into four groups, namely primary response models, structural performance models, functional performance models and damage models. The factors affecting the deterioration of the roads are very complex in nature and vary from place to place. Hence there is need to have a thorough study of the deterioration mechanism under varied climatic zones and soil conditions before arriving at a definite strategy of road improvement. Realizing the need for a detailed study involving all types of roads in the state with varying traffic and soil conditions, the present study has been attempted. This study attempts to identify the parameters that affect the performance of roads and to develop performance models suitable to Kerala conditions. A critical review of the various factors that contribute to the pavement performance has been presented based on the data collected from selected road stretches and also from five corporations of Kerala. These roads represent the urban conditions as well as National Highways, State Highways and Major District Roads in the sub urban and rural conditions. This research work is a pursuit towards a study of the road condition of Kerala with respect to varying soil, traffic and climatic conditions, periodic performance evaluation of selected roads of representative types and development of distress prediction models for roads of Kerala. In order to achieve this aim, the study is focused into 2 parts. The first part deals with the study of the pavement condition and subgrade soil properties of urban roads distributed in 5 Corporations of Kerala; namely Thiruvananthapuram, Kollam, Kochi, Thrissur and Kozhikode. From selected 44 roads, 68 homogeneous sections were studied. The data collected on the functional and structural condition of the surface include pavement distress in terms of cracks, potholes, rutting, raveling and pothole patching. The structural strength of the pavement was measured as rebound deflection using Benkelman Beam deflection studies. In order to collect the details of the pavement layers and find out the subgrade soil properties, trial pits were dug and the in-situ field density was found using the Sand Replacement Method. Laboratory investigations were carried out to find out the subgrade soil properties, soil classification, Atterberg limits, Optimum Moisture Content, Field Moisture Content and 4 days soaked CBR. The relative compaction in the field was also determined. The traffic details were also collected by conducting traffic volume count survey and axle load survey. From the data thus collected, the strength of the pavement was calculated which is a function of the layer coefficient and thickness and is represented as Structural Number (SN). This was further related to the CBR value of the soil and the Modified Structural Number (MSN) was found out. The condition of the pavement was represented in terms of the Pavement Condition Index (PCI) which is a function of the distress of the surface at the time of the investigation and calculated in the present study using deduct value method developed by U S Army Corps of Engineers. The influence of subgrade soil type and pavement condition on the relationship between MSN and rebound deflection was studied using appropriate plots for predominant types of soil and for classified value of Pavement Condition Index. The relationship will be helpful for practicing engineers to design the overlay thickness required for the pavement, without conducting the BBD test. Regression analysis using SPSS was done with various trials to find out the best fit relationship between the rebound deflection and CBR, and other soil properties for Gravel, Sand, Silt & Clay fractions. The second part of the study deals with periodic performance evaluation of selected road stretches representing National Highway (NH), State Highway (SH) and Major District Road (MDR), located in different geographical conditions and with varying traffic. 8 road sections divided into 15 homogeneous sections were selected for the study and 6 sets of continuous periodic data were collected. The periodic data collected include the functional and structural condition in terms of distress (pothole, pothole patch, cracks, rutting and raveling), skid resistance using a portable skid resistance pendulum, surface unevenness using Bump Integrator, texture depth using sand patch method and rebound deflection using Benkelman Beam. Baseline data of the study stretches were collected as one time data. Pavement history was obtained as secondary data. Pavement drainage characteristics were collected in terms of camber or cross slope using camber board (slope meter) for the carriage way and shoulders, availability of longitudinal side drain, presence of valley, terrain condition, soil moisture content, water table data, High Flood Level, rainfall data, land use and cross slope of the adjoining land. These data were used for finding out the drainage condition of the study stretches. Traffic studies were conducted, including classified volume count and axle load studies. From the field data thus collected, the progression of each parameter was plotted for all the study roads; and validated for their accuracy. Structural Number (SN) and Modified Structural Number (MSN) were calculated for the study stretches. Progression of the deflection, distress, unevenness, skid resistance and macro texture of the study roads were evaluated. Since the deterioration of the pavement is a complex phenomena contributed by all the above factors, pavement deterioration models were developed as non linear regression models, using SPSS with the periodic data collected for all the above road stretches. General models were developed for cracking progression, raveling progression, pothole progression and roughness progression using SPSS. A model for construction quality was also developed. Calibration of HDM–4 pavement deterioration models for local conditions was done using the data for Cracking, Raveling, Pothole and Roughness. Validation was done using the data collected in 2013. The application of HDM-4 to compare different maintenance and rehabilitation options were studied considering the deterioration parameters like cracking, pothole and raveling. The alternatives considered for analysis were base alternative with crack sealing and patching, overlay with 40 mm BC using ordinary bitumen, overlay with 40 mm BC using Natural Rubber Modified Bitumen and an overlay of Ultra Thin White Topping. Economic analysis of these options was done considering the Life Cycle Cost (LCC). The average speed that can be obtained by applying these options were also compared. The results were in favour of Ultra Thin White Topping over flexible pavements. Hence, Design Charts were also plotted for estimation of maximum wheel load stresses for different slab thickness under different soil conditions. The design charts showed the maximum stress for a particular slab thickness and different soil conditions incorporating different k values. These charts can be handy for a design engineer. Fuzzy rule based models developed for site specific conditions were compared with regression models developed using SPSS. The Riding Comfort Index (RCI) was calculated and correlated with unevenness to develop a relationship. Relationships were developed between Skid Number and Macro Texture of the pavement. The effort made through this research work will be helpful to highway engineers in understanding the behaviour of flexible pavements in Kerala conditions and for arriving at suitable maintenance and rehabilitation strategies. Key Words: Flexible Pavements – Performance Evaluation – Urban Roads – NH – SH and other roads – Performance Models – Deflection – Riding Comfort Index – Skid Resistance – Texture Depth – Unevenness – Ultra Thin White Topping

Framework for middleware executed on mobile devices

Die ubiquitäre Datenverarbeitung ist ein attraktives Forschungsgebiet des vergangenen und aktuellen Jahrzehnts. Es handelt von unaufdringlicher Unterstützung von Menschen in ihren alltäglichen Aufgaben durch Rechner. Diese Unterstützung wird durch die Allgegenwärtigkeit von Rechnern ermöglicht die sich spontan zu verteilten Kommunikationsnetzwerken zusammen finden, um Informationen auszutauschen und zu verarbeiten. Umgebende Intelligenz ist eine Anwendung der ubiquitären Datenverarbeitung und eine strategische Forschungsrichtung der Information Society Technology der Europäischen Union. Das Ziel der umbebenden Intelligenz ist komfortableres und sichereres Leben. Verteilte Kommunikationsnetzwerke für die ubiquitäre Datenverarbeitung charakterisieren sich durch Heterogenität der verwendeten Rechner. Diese reichen von Kleinstrechnern, eingebettet in Gegenstände des täglichen Gebrauchs, bis hin zu leistungsfähigen Großrechnern. Die Rechner verbinden sich spontan über kabellose Netzwerktechnologien wie wireless local area networks (WLAN), Bluetooth, oder UMTS. Die Heterogenität verkompliziert die Entwicklung und den Aufbau von verteilten Kommunikationsnetzwerken. Middleware ist eine Software Technologie um Komplexität durch Abstraktion zu einer homogenen Schicht zu reduzieren. Middleware bietet eine einheitliche Sicht auf die durch sie abstrahierten Ressourcen, Funktionalitäten, und Rechner. Verteilte Kommunikationsnetzwerke für die ubiquitäre Datenverarbeitung sind durch die spontane Verbindung von Rechnern gekennzeichnet. Klassische Middleware geht davon aus, dass Rechner dauerhaft miteinander in Kommunikationsbeziehungen stehen. Das Konzept der dienstorienterten Architektur ermöglicht die Entwicklung von Middleware die auch spontane Verbindungen zwischen Rechnern erlaubt. Die Funktionalität von Middleware ist dabei durch Dienste realisiert, die unabhängige Software-Einheiten darstellen. Das Wireless World Research Forum beschreibt Dienste die zukünftige Middleware beinhalten sollte. Diese Dienste werden von einer Ausführungsumgebung beherbergt. Jedoch gibt es noch keine Definitionen wie sich eine solche Ausführungsumgebung ausprägen und welchen Funktionsumfang sie haben muss. Diese Arbeit trägt zu Aspekten der Middleware-Entwicklung für verteilte Kommunikationsnetzwerke in der ubiquitären Datenverarbeitung bei. Der Schwerpunkt liegt auf Middleware und Grundlagentechnologien. Die Beiträge liegen als Konzepte und Ideen für die Entwicklung von Middleware vor. Sie decken die Bereiche Dienstfindung, Dienstaktualisierung, sowie Verträge zwischen Diensten ab. Sie sind in einem Rahmenwerk bereit gestellt, welches auf die Entwicklung von Middleware optimiert ist. Dieses Rahmenwerk, Framework for Applications in Mobile Environments (FAME²) genannt, beinhaltet Richtlinien, eine Definition einer Ausführungsumgebung, sowie Unterstützung für verschiedene Zugriffskontrollmechanismen um Middleware vor unerlaubter Benutzung zu schützen. Das Leistungsspektrum der Ausführungsumgebung von FAME² umfasst: • minimale Ressourcenbenutzung, um auch auf Rechnern mit wenigen Ressourcen, wie z.B. Mobiltelefone und Kleinstrechnern, nutzbar zu sein • Unterstützung für die Anpassung von Middleware durch Änderung der enthaltenen Dienste während die Middleware ausgeführt wird • eine offene Schnittstelle um praktisch jede existierende Lösung für das Finden von Diensten zu verwenden • und eine Möglichkeit der Aktualisierung von Diensten zu deren Laufzeit um damit Fehlerbereinigende, optimierende, und anpassende Wartungsarbeiten an Diensten durchführen zu können Eine begleitende Arbeit ist das Extensible Constraint Framework (ECF), welches Design by Contract (DbC) im Rahmen von FAME² nutzbar macht. DbC ist eine Technologie um Verträge zwischen Diensten zu formulieren und damit die Qualität von Software zu erhöhen. ECF erlaubt das aushandeln sowie die Optimierung von solchen Verträgen.

A Framework for TEI-Based Scholarly Text Editions

In this paper, we describe an interdisciplinary project in which visualization techniques were developed for and applied to scholarly work from literary studies. The aim was to bring Christof Schöch's electronic edition of Bérardier de Bataut's Essai sur le récit (1776) to the web. This edition is based on the Text Encoding Initiative's XML-based encoding scheme (TEI P5, subset TEI-Lite). This now de facto standard applies to machine-readable texts used chiefly in the humanities and social sciences. The intention of this edition is to make the edited text freely available on the web, to allow for alternative text views (here original and modern/corrected text), to ensure reader-friendly annotation and navigation, to permit on-line collaboration in encoding and annotation as well as user comments, all in an open source, generically usable, lightweight package. These aims were attained by relying on a GPL-based, public domain CMS (Drupal) and combining it with XSL-Stylesheets and Java Script.

Design and Control of an Anthropomorphic Robotic Finger with Multi-point Tactile Sensation

The goal of this research is to develop the prototype of a tactile sensing platform for anthropomorphic manipulation research. We investigate this problem through the fabrication and simple control of a planar 2-DOF robotic finger inspired by anatomic consistency, self-containment, and adaptability. The robot is equipped with a tactile sensor array based on optical transducer technology whereby localized changes in light intensity within an illuminated foam substrate correspond to the distribution and magnitude of forces applied to the sensor surface plane. The integration of tactile perception is a key component in realizing robotic systems which organically interact with the world. Such natural behavior is characterized by compliant performance that can initiate internal, and respond to external, force application in a dynamic environment. However, most of the current manipulators that support some form of haptic feedback either solely derive proprioceptive sensation or only limit tactile sensors to the mechanical fingertips. These constraints are due to the technological challenges involved in high resolution, multi-point tactile perception. In this work, however, we take the opposite approach, emphasizing the role of full-finger tactile feedback in the refinement of manual capabilities. To this end, we propose and implement a control framework for sensorimotor coordination analogous to infant-level grasping and fixturing reflexes. This thesis details the mechanisms used to achieve these sensory, actuation, and control objectives, along with the design philosophies and biological influences behind them. The results of behavioral experiments with a simple tactilely-modulated control scheme are also described. The hope is to integrate the modular finger into an %engineered analog of the human hand with a complete haptic system.

A HOLISTIC APPROACH TO MANUFACTURING SYSTEM DESIGN IN THE DEFENSE AEROSPACE INDUSTRY

Manufacturing has evolved to become a critical element of the competitive skill set of defense aerospace firms. Given the changes in the acquisition environment and culture; traditional “thrown over the wall” means of developing and manufacturing products are insufficient. Also, manufacturing systems are complex systems that need to be carefully designed in a holistic manner and there are shortcomings with available tools and methods to assist in the design of these systems. This paper outlines the generation and validation of a framework to guide this manufacturing system design process.

Lifecycle Value Framework for Tactical Aircraft Product Development

Due to a dramatic reduction in defense procurement, the benchmark for developing new defense systems today is performance at an affordable cost. In an attempt to encircle a more holistic perspective of value, lifecycle value has evolved as a concept within the Lean Aerospace Initiative, LAI. The implication of this is development of products incorporating lifecycle and long-term focus instead of a shortsighted cost cutting focus. The interest to reduce total cost of ownership while still improving performance, availability, and sustainability, other dimensions taken into account within the lifecycle value approach, falls well within this context. Several factors prevent enterprises from having a holistic perspective during product development. Some important aspects are increased complexity of the products and significant technological uncertainty. The combination of complexity in system design and the limits of individual human comprehension typically prevent a best value solution to be envisioned. The purpose of this research was to examine relative contributions in product development and determine factors that significantly promote abilities to consider and achieve lifecycle value. This paper contributes a maturity matrix based on important practices and lessons learned through extensive interview based case studies of three tactical aircraft programs, including experiences from more than 100 interviews.

A Holistic Approach to Manufacturing System Design in the Defense Aerospace Industry

Manufacturing has evolved to become a critical element of the competitive skill set of defense aerospace firms. Given the changes in the acquisition environment and culture; traditional “thrown over the wall” means of developing and manufacturing products are insufficient. Also, manufacturing systems are complex systems that need to be carefully designed in a holistic manner and there are shortcomings with available tools and methods to assist in the design of these systems. This paper outlines the generation and validation of a framework to guide this manufacturing system design process.

Decentralized model reference control of flexible cable-stayed beam structures

A decentralized model reference controller is designed to reduce the magnitude of the transversal vibration of a flexible cable-stayed beam structure induced by a seismic excitation. The controller design is made based on the principle of sliding mode such that a priori knowledge

A mixed H2/H∞-based semiactive control for vibration mitigation in flexible structures

In this paper, we address this problem through the design of a semiactive controller based on the mixed H2/H∞ control theory. The vibrations caused by the seismic motions are mitigated by a semiactive damper installed in the bottom of the structure. It is meant by semiactive damper, a device that absorbs but cannot inject energy into the system. Sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities (LMIs). A controller that guarantees asymptotic stability and a mixed H2/H∞ performance is then developed. An algorithm is proposed to handle the semiactive nature of the actuator. The performance of the controller is experimentally evaluated in a real-time hybrid testing facility that consists of a physical specimen (a small-scale magnetorheological damper) and a numerical model (a large-scale three-story building)

The UK Professional Standards Framework for teaching and supporting learning in higher education

The UK Professional Standards Framework (UK PSF) for teaching and supporting learning, launched in February 2006, is a flexible framework which uses a descriptor-based approach to professional standards. There are three standard descriptors each of which is applicable to a number of staff roles and to different career stages of those engaged in teaching and supporting learning. The standard descriptors are underpinned by areas of professional activity, core knowledge and professional values. The framework provides a reference point for institutions and individuals as well as supporting ongoing development within any one standard descriptor.

FAIA : framework para la enseñanza de agentes en IA.

Resumen tomado del autor

El Outsourcing en la dinámica de sistemas hacia mercados extranjeros

Este trabajo recopila literatura académica relevante sobre estrategias de entrada y metodologías para la toma de decisión sobre la contratación de servicios de Outsourcing para el caso de empresas que planean expandirse hacia mercados extranjeros. La manera en que una empresa planifica su entrada a un mercado extranjero, y realiza la consideración y evaluación de información relevante y el diseño de la estrategia, determina el éxito o no de la misma. De otro lado, las metodologías consideradas se concentran en el nivel estratégico de la pirámide organizacional. Se parte de métodos simples para llegar a aquellos basados en la Teoría de Decisión Multicriterio, tanto individuales como híbridos. Finalmente, se presenta la Dinámica de Sistemas como herramienta valiosa en el proceso, por cuanto puede combinarse con métodos multicriterio.

Forms of participatory democracy: an analytical framework based on the experiences of Bolivia, brazil and Colombia

Based on the experiences of Colombia, Brazil and Bolivia, the paper proposes a general analytical framework for participatory mechanisms. The analysis is oriented to detect the incentives in each system and theethics and behavior sustaining them. It investigates about the sustainability of participatory democracy, in the face of tensions with representative democracy. The article presents a theoretical framework built from theseexperiences of institutional design and political practice, and confronts it against the theoretical conceptualizationsof participatory democracy in Bobbio, Sartori, Elster and Nino, among others. In this context, different waysin which those schemes can be inserted in the political systems become apparent, along with the variables thatresult from combining elements of direct, representative and participatory democracy”

A formalization for multi-agent decision support in cooperative environments. A framework for situated agents

La tesis propone un marco de trabajo para el soporte de la toma de decisiones adecuado para soportar la ejecución distribuida de acciones cooperativas en entornos multi-agente dinámicos y complejos. Soporte para la toma de decisiones es un proceso que intenta mejorar la ejecución de la toma de decisiones en escenarios cooperativos. Este proceso ocurre continuamente en la vida diaria. Los humanos, por ejemplo, deben tomar decisiones acerca de que ropa usar, que comida comer, etc. En este sentido, un agente es definido como cualquier cosa que está situada en un entorno y que actúa, basado en su observación, su interpretación y su conocimiento acerca de su situación en tal entorno para lograr una acción en particular.Por lo tanto, para tomar decisiones, los agentes deben considerar el conocimiento que les permita ser consientes en que acciones pueden o no ejecutar. Aquí, tal proceso toma en cuenta tres parámetros de información con la intención de personificar a un agente en un entorno típicamente físico. Así, el mencionado conjunto de información es conocido como ejes de decisión, los cuales deben ser tomados por los agentes para decidir si pueden ejecutar correctamente una tarea propuesta por otro agente o humano. Los agentes, por lo tanto, pueden hacer mejores decisiones considerando y representando apropiadamente tal información. Los ejes de decisión, principalmente basados en: las condiciones ambientales, el conocimiento físico y el valor de confianza del agente, provee a los sistemas multi-agente un confiable razonamiento para alcanzar un factible y exitoso rendimiento cooperativo.Actualmente, muchos investigadores tienden a generar nuevos avances en la tecnología agente para incrementar la inteligencia, autonomía, comunicación y auto-adaptación en escenarios agentes típicamente abierto y distribuidos. En este sentido, esta investigación intenta contribuir en el desarrollo de un nuevo método que impacte tanto en las decisiones individuales como colectivas de los sistemas multi-agente. Por lo tanto, el marco de trabajo propuesto ha sido utilizado para implementar las acciones concretas involucradas en el campo de pruebas del fútbol robótico. Este campo emula los juegos de fútbol real, donde los agentes deben coordinarse, interactuar y cooperar entre ellos para solucionar tareas complejas dentro de un escenario dinámicamente cambiante y competitivo, tanto para manejar el diseño de los requerimientos involucrados en las tareas como para demostrar su efectividad en trabajos colectivos. Es así que los resultados obtenidos tanto en el simulador como en el campo real de experimentación, muestran que el marco de trabajo para el soporte de decisiones propuesto para agentes situados es capaz de mejorar la interacción y la comunicación, reflejando en un adecuad y confiable trabajo en equipo dentro de entornos impredecibles, dinámicos y competitivos. Además, los experimentos y resultados también muestran que la información seleccionada para generar los ejes de decisión para situar a los agentes, es útil cuando tales agentes deben ejecutar una acción o hacer un compromiso en cada momento con la intención de cumplir exitosamente un objetivo colectivo. Finalmente, algunas conclusiones enfatizando las ventajas y utilidades del trabajo propuesto en la mejora del rendimiento colectivo de los sistemas multi-agente en situaciones tales como tareas coordinadas y asignación de tareas son presentadas.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.