Studies on IL-18 in HIV infection : effects of the cytokine on intestinal integrity, and platelets as a new source of the cytokine

L'interleukine IL-18 (IL-18), un membre de la famille de l’IL-1, est une cytokine pro-inflammatoire multifonctionnelle. Elle est produite par les monocytes, les macrophages, les cellules dendritiques, les cellules épithéliales, les kératinocytes et le cortex surrénal dans le corps humain. Cette cytokine est d'abord produite comme une protéine précurseure inactive, qui est par la suite clivée en une forme mature par la caspase-1 activée. La caspase, en elle-même, existe comme précurseur inactif dans les cellules humaines et requiert l'assemblage d'inflammasomes pour son activation. L'IL-18 pour joue un rôle clé dans la médiation des conditions inflammatoires. Notre laboratoire et d'autres ont montré que l'infection par le VIH est accompagnée d'une augmentation des taux circulants d'IL-18 avec une diminution des niveaux de son antagoniste, l'interleukine-18 binding protein (IL-18BP). Dans cette thèse, nous démontrons pour que l'IL-18 est également produite et sécrétée par les plaquettes humaines lors de leur activation. Les plaquettes contiennent des composants de l'inflammasome. Ils assemblent et activent la caspase-1, qui ensuite traite le précurseur de l'IL-18 dans sa forme mature au cours du processus d'activation des plaquettes. La cytokine est synthétisée de novo lors de l'activation des plaquettes. Contrairement à l'IL-18, les plaquettes expriment constitutivement l’IL-18BP, et la libèrent de manière constitutive, ainsi que lors de l'activation. L'IL-18 et l'IL-18BP sont colocalisés avec CD63, un marqueur pour les granules α des plaquettes. L'IL-18 libéré des plaquettes constitue la source principale de cette cytokine dans la circulation humaine chez les individus sains. Nous avons identifié des concentrations faibles de cette cytokine dans les lysats de plaquettes chez les individus infectés par le VIH par rapport à ceux en santé. D'autre part, les concentrations ont été augmentées dans le sérum et le plasma pauvre en plaquettes chez les individus infectés. Des résultats similaires ont été obtenus avec l'IL-18BP dans les lysats de plaquettes d'individus sains et infectés par le VIH. Cependant, des quantités plus faibles de cet antagoniste ont été trouvées dans le sérum et le plasma pauvre en plaquettes d'individus infectés par le VIH par rapport à ceux en santé. Nos résultats ont des implications importantes pour les maladies inflammatoires chroniques dans laquelle une activité accrue de l'IL-18 joue un rôle pathogène. Le VIH est également accompagné par une inflammation intestinale et une diminution de l'intégrité intestinale, mesurée par la réparation de la muqueuse, la régénération et la perméabilité. Cependant, on en sait peu sur la relation entre le niveau élevé de l'IL-18 associé à l'infection au VIH et la perméabilité intestinale: ceci n'a jamais été étudié. Dans cette thèse, nous démontrons le rôle du virus et sa protéine Tat à augmenter la production d'IL-18 chez deux lignées de cellules épithéliales intestinales (HT29 et Caco2) ainsi qu'une diminution de l'IL-18BP. L'IL-18 induit une hyperperméabilité de la barrière épithéliale en perturbant à la fois les jonctions serrées et adhérentes, et ce, en modulant l'expression et la distribution de l'occludine, de claudine-2 et de la bêta-caténine. Une désorganisation de l'actine F a également été observée dans les cellules lors de l'incubation avec l'IL-18. Les mêmes observations ont été faites avec la protéine Tat du VIH-1. Après une incubation prolongée, l'IL-18 a causé la mort des cellules intestinales et induit l'apoptose par l'activation de la caspase-1 et la caspase-3. Fait intéressant, les taux plasmatiques de lipopolysaccharides chez trois catégories différentes de patients au VIH (ART-naïf, ART-traitée et contrôleurs élite) sont en corrélation avec les niveaux plasmatiques de l'IL-18. Enfin, nous avons étudié la voie de signalisation à travers laquelle l'IL-18 induit une perméabilité intestinale accrue. En bref, nos études identifient les plaquettes comme une source importante d'IL-18, et leur activation lors d'une infection à VIH contribue à des concentrations accrues de cette cytokine. Le virus entraine également l'augmentation de la production de cytokines par les cellules épithéliales intestinales. L'activité biologique accrue de ces cytokines contribue à la pathogenèse du sida en augmentant la perméabilité intestinale et en causant la mort des cellules intestinales. L'IL-18 pourrait servir de cible moléculaire pour retarder la progression du sida et réduire l'inflammation chronique dans un stade précoce d'une infection à VIH.

Étude de la migration des populations de lymphocytes B du sang de patients infectés par le virus d’immunodéficience humaine (VIH)

La dérégulation du compartiment de cellules B est une conséquence importante de l’infection par le virus de l’immunodéficience humaine (VIH-1). On observe notamment une diminution des nombres de lymphocytes B sanguins ainsi qu’une variation des fréquences relatives des différentes populations de lymphocytes B chez les individus infectés par rapport aux contrôles sains. Notre laboratoire a précédemment démontré l’implication des cellules dendritiques dans la dérégulation des lymphocytes B via la roduction excessive de BLyS/BAFF, un stimulateur des cellules B. De plus, lors l’études menées chez la souris transgénique présentant une maladie semblable au SIDA, et chez la souris BLyS/BAFF transgénique, l’infection au VIH-1 fut associée à une expansion de la zone marginale (MZ) de la rate. De façon intéressante, nous observons chez les contrôleurs élites une diminution de la population B ‘mature’ de la MZ. Il s’agit du seul changement important chez les contrôleurs élites et reflète possiblement un recrutement de ces cellules vers la périphérie ainsi qu’une implication dans des mécanismes de contrôle de l’infection. Pour tenter d’expliquer et de mieux comprendre ces variations dans les fréquences des populations B, nous avons analysé les axes chimiotactiques CXCL13-CXCR5, CXCL12-CXCR4/CXCR7, CCL20-CCR6 et CCL25-CCR9. L’étude longitudinale de cohortes de patients avec différents types de progression clinique ou de contrôle de l’infection démontre une modulation des niveaux plasmatiques de la majorité des chimiokines analysées chez les progresseurs rapides et classiques. Au contraire, les contrôleurs élites conservent des niveaux normaux de chimiokines, démontrant leur capacité à maintenir l’homéostasie. La migration des populations de cellules B semble être modulée selon la progression ou le contrôle de l’infection. Les contrôleurs élites présentent une diminution de la population B ‘mature’ de la MZ et une augmentation de la fréquence d’expression du récepteur CXCR7 associé à la MZ chez la souris, suggérant un rôle important des cellules de la MZ dans le contrôle de l’infection au VIH-1. De façon générale, les résultats dans cette étude viennent enrichir nos connaissances du compartiment de cellules B dans le contexte de l’infection au VIH-1 et pourront contribuer à élaborer des stratégies préventives et thérapeutiques contre ce virus.

Studies on the isolation and characterization of flavones and triterpenoids from a few plants

In the present scenario, there is an increasing demand for natural products in food industry, pharmaceuticals, cosmetics and agricultural sectors. In this context phytochemical study to identify newer chemicals has got great relevance. Phytochemical studies have become more reliable and encouraging with the development of modern analytical techniques.In the present work the leaves of Piper colubrinum (Piperaceae), aerial parts of Mussaenda fiondosa (Rubiaceae) and Humboldtia vahliana (Leguminosae) and the pericarp of fruits of Artocarpus heterophyllus (Moraceae) were investigated for their secondary metabolites. The major compounds isolated belong to the groups of flavonoids and triterpenoids.Naturally occurring flavonoids have been used widely in chemotaxonomic studies of plants. Flavones and flavonols constitute a group of biosynthetically related natural products. No universal function has been established for flavones and flavonols in plants. However, many functions in individual plants have been demonstrated. These include protection of plants from ultraviolet light, insects and pests; pollinator attractants; antioxidants; plant hormone controllers; enzyme inhibitors and allelopathic agents. Flavonoids are attracting the attention of medical scientists in recent years because of their anticarcinogenic, antiallergic and antiinflammatory properties. The recent discovery that flavonoids are involved in the process of nitrogen fixation in plants also opens the way for agricultural application of these constituents.Triterpenoids are another class of compounds that are ubiquitous in plants. Some triterpenoids present in the latex and resins of plants are believed to be involved in chemical defence against pathogens and herbivores. Triterpenoids possess various biological properties including anti-inflammatory, antifeedant, pesticidal, fungitoxic and antimicrobial activities. Triterpenoids with cytotoxic activity and inhibitory effect on seed germination are also known.

Evaluation of the Power Consumption of Routing Protocols for Wireless Sensor Networks

Sensor networks are one of the fastest growing areas in broad of a packet is in transit at any one time. In GBR, each node in the network can look at itsneighbors wireless ad hoc networking (? Eld. A sensor node, typically'hop count (depth) and use this to decide which node to forward contains signal-processing circuits, micro-controllers and a the packet on to. If the nodes' power level drops below a wireless transmitter/receiver antenna. Energy saving is one certain level it will increase the depth to discourage trafiE of the critical issue for sensor networks since most sensors are equipped with non-rechargeable batteries that have limitedlifetime. Routing schemes are used to transfer data collectedby sensor nodes to base stations. In the literature many routing protocols for wireless sensor networks are suggested. In this work, four routing protocols for wireless sensor networks viz Flooding, Gossiping, GBR and LEACH have been simulated using TinyOS and their power consumption is studied using PowerTOSSIM. A realization of these protocols has beencarried out using Mica2 Motes.

Evaluation of the Power Consumption of Routing Protocols for Wireless Sensor Networks

Sensor networks are one of the fastest growing areas in broad of a packet is in transit at any one time. In GBR, each node in the network can look at itsneighbors wireless ad hoc networking (? Eld. A sensor node, typically'hop count (depth) and use this to decide which node to forward contains signal-processing circuits, micro-controllers and a the packet on to. If the nodes' power level drops below a wireless transmitter/receiver antenna. Energy saving is one certain level it will increase the depth to discourage trafiE of the critical issue forfor sensor networks since most sensors are equipped with non-rechargeable batteries that have limited lifetime.

Evaluation of the Power Consumption of Routing Protocols for Wireless Sensor Networks

Sensor networks are one of the fastest growing areas in broadwireless ad hoc networking (?Eld. A sensor node, typically'contains signal-processing circuits, micro-controllers and awireless transmitter/receiver antenna. Energy saving is oneof the critical issue for sensor networks since most sensorsare equipped with non-rechargeable batteries that have limited lifetime.In thiswork, four routing protocols for wireless sensor networks vizFlooding, Gossiping, GBR and LEACH have been simulated using Tiny OS and their power consumption is studied usingcaorwreiredTOoSuStIuMs.ingAMirceaal2izMaotitoens.of these protocols has been carried out using mica 2 motes

Gewerbeaufsicht im 21. Jahrhundert.

Während zum Genehmigungsrecht zahlreiche Abhandlungen in der juristischen Literatur und eine große Zahl von Urteilen veröffentlicht sind, hält sich die Forschung und praktische Behandlung zum Aufsichtsrecht in Grenzen. Diese Arbeit vertieft das Verständnis, für die spezifische Verknüpfung und gegenseitige Abhängigkeit der Eröffnungskontrollen und der begleitenden Kontrollen im deutschen Arbeits-, Umwelt- und Verbraucherschutzrecht. Zentraler Punkt dieser Arbeit ist die Entwicklung von Grundlinien der begleitenden Aufsicht im Gewerbeaufsichtsrecht. Dazu ist es erforderlich die verschiedenen Randbedingungen gewerbeaufsichtlichen Handelns in den Blick zu nehmen. Es ist ein Blick auf die zu erwartende Ausbildung eines neuen Rationalitätstyps der gesellschaftlichen Entwicklung (2.), auf die Typisierung von Staats-, Gewerbe- und Wirtschaftsaufsicht und deren spezifischen Handlungsmustern, den festgestellten Defiziten des Aufsichtsrechts und des Aufsichtshandelns der begleitenden Kontrollen und den festgestellten tatsächlichen Wirkungen des Aufsichtssystems (3.) zu werfen. Weitere Einflüsse auf das Aufsichtsmodell der Zukunft kommen aus der erwarteten und wünschenswerten Entwicklung des Genehmigungsrechts (4.), der Art und Weise wie die begleitende Aufsicht gehandhabt werden kann und soll (5.) und den Privatisierungstypen und deren verfassungsrechtlichen Grenzen (6.). Die Arbeit schließt mit der Formulierung eines Zukunftsmodells, dass die Gewichte zwischen der Eröffnungs- und der begleitender Kontrolle, sowie das Verhältnis zwischen Staat, Privaten Dritten und Unternehmen, neu ordnet. Insgesamt wird in dieser Arbeit für ein Aufsichtsmodell plädiert, indem der Staat stärker in die Verantwortung für eine risikoorientierte begleitende Aufsicht genommen wird. Maßstäbe für die Risikoregelung sind künftig komplett vom Staat aufzustellen. Staatliche Aufsicht kann sich zukünftig auf Rahmenregelungen und Rahmenprüfungen bei den risikoreichsten Anlagen, Tätigkeiten und Produkten beschränken. Private Dritte können die Detailermittlungen und Freigaben bearbeiten. Private Sachverständige können künftig die Hauptlast detaillierter und zeitintensiver Kontrolltätigkeiten bei Anlagen, Tätigkeiten und Produkten mit mittlerem Risiko übernehmen. Anlagen, Tätigkeiten und Produkte mit geringem Risiko können der Eigenüberwachung überlassen werden. Im Gegenzug muss der Staat in deutlich stärkeren Maß die Aufsicht über die Kontrolleure anhand einheitlicher Maßstäbe organisieren und durchführen. Die Anforderungen an die Kontrolleure müssen künftig allgemein, sowohl für die externen Kontrollpersonen als auch für die internen Aufsichtspersonen, gelten und überprüft werden.

Virtual Model Control of a Hexapod Walking Robot

Since robots are typically designed with an individual actuator at each joint, the control of these systems is often difficult and non-intuitive. This thesis explains a more intuitive control scheme called Virtual Model Control. This thesis also demonstrates the simplicity and ease of this control method by using it to control a simulated walking hexapod. Virtual Model Control uses imagined mechanical components to create virtual forces, which are applied through the joint torques of real actuators. This method produces a straightforward means of controlling joint torques to produce a desired robot behavior. Due to the intuitive nature of this control scheme, the design of a virtual model controller is similar to the design of a controller with basic mechanical components. The ease of this control scheme facilitates the use of a high level control system which can be used above the low level virtual model controllers to modulate the parameters of the imaginary mechanical components. In order to apply Virtual Model Control to parallel mechanisms, a solution to the force distribution problem is required. This thesis uses an extension of Gardner`s Partitioned Force Control method which allows for the specification of constrained degrees of freedom. This virtual model control technique was applied to a simulated hexapod robot. Although the hexapod is a highly non-linear, parallel mechanism, the virtual models allowed text-book control solutions to be used while the robot was walking. Using a simple linear control law, the robot walked while simultaneously balancing a pendulum and tracking an object.

A Hierarchical Cache Coherent Protocol

As the number of processors in distributed-memory multiprocessors grows, efficiently supporting a shared-memory programming model becomes difficult. We have designed the Protocol for Hierarchical Directories (PHD) to allow shared-memory support for systems containing massive numbers of processors. PHD eliminates bandwidth problems by using a scalable network, decreases hot-spots by not relying on a single point to distribute blocks, and uses a scalable amount of space for its directories. PHD provides a shared-memory model by synthesizing a global shared memory from the local memories of processors. PHD supports sequentially consistent read, write, and test- and-set operations. This thesis also introduces a method of describing locality for hierarchical protocols and employs this method in the derivation of an abstract model of the protocol behavior. An embedded model, based on the work of Johnson[ISCA19], describes the protocol behavior when mapped to a k-ary n-cube. The thesis uses these two models to study the average height in the hierarchy that operations reach, the longest path messages travel, the number of messages that operations generate, the inter-transaction issue time, and the protocol overhead for different locality parameters, degrees of multithreading, and machine sizes. We determine that multithreading is only useful for approximately two to four threads; any additional interleaving does not decrease the overall latency. For small machines and high locality applications, this limitation is due mainly to the length of the running threads. For large machines with medium to low locality, this limitation is due mainly to the protocol overhead being too large. Our study using the embedded model shows that in situations where the run length between references to shared memory is at least an order of magnitude longer than the time to process a single state transition in the protocol, applications exhibit good performance. If separate controllers for processing protocol requests are included, the protocol scales to 32k processor machines as long as the application exhibits hierarchical locality: at least 22% of the global references must be able to be satisfied locally; at most 35% of the global references are allowed to reach the top level of the hierarchy.

Reinforcement Learning by Policy Search

One objective of artificial intelligence is to model the behavior of an intelligent agent interacting with its environment. The environment's transformations can be modeled as a Markov chain, whose state is partially observable to the agent and affected by its actions; such processes are known as partially observable Markov decision processes (POMDPs). While the environment's dynamics are assumed to obey certain rules, the agent does not know them and must learn. In this dissertation we focus on the agent's adaptation as captured by the reinforcement learning framework. This means learning a policy---a mapping of observations into actions---based on feedback from the environment. The learning can be viewed as browsing a set of policies while evaluating them by trial through interaction with the environment. The set of policies is constrained by the architecture of the agent's controller. POMDPs require a controller to have a memory. We investigate controllers with memory, including controllers with external memory, finite state controllers and distributed controllers for multi-agent systems. For these various controllers we work out the details of the algorithms which learn by ascending the gradient of expected cumulative reinforcement. Building on statistical learning theory and experiment design theory, a policy evaluation algorithm is developed for the case of experience re-use. We address the question of sufficient experience for uniform convergence of policy evaluation and obtain sample complexity bounds for various estimators. Finally, we demonstrate the performance of the proposed algorithms on several domains, the most complex of which is simulated adaptive packet routing in a telecommunication network.

Semiactive backstepping control for vibration attenuation in structures equipped with magnetorheological actuatorscat

This paper deals with the problem of semiactive vibration control of civil engineering structures subject to unknown external disturbances (for example, earthquakes, winds, etc.). Two kinds of semiactive controllers are proposed based on the backstepping control technique. The experimental setup used is a 6-story test structure equipped with shear-mode semiactive magnetorheological dampers being installed in the Washington University Structural Control and Earthquake Engineering Laboratory (WUSCEEL). The experimental results obtained have verified the effectiveness of the proposed control algorithms

QFT control for vibration reduction in structures equipped with MR dampers

This short paper addresses the problem of designing a QFT (quantitative feedback theory) based controllers for the vibration reduction in a 6-story building structure equipped with shear-mode magnetorheological dampers. A new methodology is proposed for characterizing the nonlinear hysteretic behavior of the MR damper through the uncertainty template in the Nichols chart. The design procedure for QFT control design is briefly presented

Innovation In Games

In this lecture we look at how innovation in games has moved from the creation of new genres, to the incorporation of new technology, that has unlocked new ways to play games. In particular we look at casual and social games, motion controllers, virtual reality, augmented reality, location-based games, mixed reality, and alternate reality.

Ergonomía. Fundamentos para el desarrollo de soluciones ergonómicas

En este texto se presentan algunos conceptos y marcos teóricos útiles para el análisis del trabajo en ergonomía. El objetivo es mostrar los conceptos de base para el estudio del trabajo en la tradición de la ergonomía de la actividad, y analizar de manera general algunos de los modelos empleados para el análisis de una actividad de trabajo. Inicialmente se abordan los principios teóricos de la ergonomía y los principios que provienen de la fisiología, la biomecánica, la psicología y la sociología; también se presentan los acercamientos metodológicos empleados en esta misma perspectiva para el análisis de actividades de trabajo. Se parte del principio de que un estudio ergonómico del trabajo se puede llevar a cabo desde una doble perspectiva: la perspectiva analítica y la perspectiva comprensiva.

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.