Is Māori food sovereignty affected by adherence, or lack thereof, to Te Tiriti O Waitangi?

Māori food sovereignty was and continues to be severely affected by British colonisation and influence. This situation and its causes, both past and present, will be examined in the context of Māori culture, especially Te Tiriti, a founding document of New Zealand. The general concept of food sovereignty is introduced, and its key principle: having power over one's own food system. A brief history of Māori food systems is necessary as context–their adaptation from Polynesia to New Zealand and later, to European settlement. Te Tiriti and the Treaty of Waitangi are explained: how they were created and why Te Tiriti is authoritative. Then, different aspects of Te Tiriti are linked to various parts of Māori food sovereignty and traditional Māori concepts. Through breaching tuku whenua in Te Tiriti, land issues have arisen: the methods used to confiscate Māori land and the effects this had on traditional food, health and urbanisation are discussed. Culture as taonga is examined: the ways in which losing a food system leads to losing traditions, and how this breaches Te Tiriti. Then the (mostly negative) effects of this shift in food systems on the environment is examined, and how this relates back to taonga as well as the traditional duty of kaitiakitanga and, again, the breaching of Te Tiriti. Lastly, the underlying issue of power is examined in relation to rangatiratanga and overall sovereignty–this is also linked to Te Tiriti.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Magneto-optische Oberflächenplasmonresonanzeffekte in austauschverschobenen Dünnschichtsystemen

Die Wechselwirkungen zwischen Biomolekülen spielen eine zentrale Rolle in der biochemischen und pharmazeutischen Forschung. In der biomolekularen Interaktionsanalyse sind dabei Biosensoren auf Basis des Oberflächenplasmonresonanzeffekts (SPR-Effekt) weitverbreitet. Seit Einführung der ersten kommerziellen SPR-Biosensoren Anfang der 1990er Jahre wurden verschiedenste Messanordnungen sowie Materialsysteme mit dem Ziel einer möglichst hohen Empfindlichkeit getestet. Eine Möglichkeit zur Steigerung der Empfindlichkeit klassischer SPR-Systeme bieten sogenannte magneto-optische SPR-Biosensoren (MOSPR-Biosensoren). Grundlage der Empfindlichkeitssteigerung ist die gleichzeitige Messung des SPR-Effekts und des transversalen magneto-optischen KERR-Effekts (tMOKE). Bisherige Untersuchungen haben sich meist auf den Einfluss der Magnetisierung freier ferromagnetischer Schichten beschränkt. Im Rahmen dieser Arbeit wurden erstmals austauschverschobene Dünnschichtsysteme (EB-Systeme), eine Kombination aus Ferromagnet und Antiferromagnet, hinsichtlich ihrer Eignung für SPR- und MOSPR-basierte biosensorische Anwendungen untersucht. Aufgrund der remanenten Magnetisierung der ferromagnetischen Schicht und ihrer magnetischen Strukturierbarkeit sind EB-Systeme eine hochinteressante Plattform zur Realisierung neuer Biosensorkonzepte. Zur Reduzierung der stark dämpfendenden Wirkung magnetischer Materialien wurde das hier betrachtete IrMn/Co EB-System zwischen zwei Goldschichten eingebettet. Eine Gegenüberstellung optimierter Au/ IrMn/Co/Au-Systeme mit einem reinen Au-System, wie es typischerweise in kommerziellen SPR-basierten Biosensoren eingesetzt wird, demonstriert, dass mit den entwickelten EB-Systemen vergleichbare Empfindlichkeiten in SPR-Sensor-Anwendungen erreicht werden können. Die magneto-optische Aktivität der untersuchten Dünnschichtsysteme liegt im Bereich der Literaturwerte für Au/Co/Au-Systeme, mit denen erhöhte Empfindlichkeiten gegenüber Standard-SPR-Biosensoren realisiert wurden. Auf Grundlage magnetisch strukturierter Au/IrMn/Co/Au-Systeme wurden neue Biosensorkonzepte entwickelt und getestet. Erste Experimente belegen, dass mit diesen Schichtsystemen eine gleichzeitige Detektion der magnetisierungsabhängigen Reflektivitäten in ortsauflösenden MOSPR-Messungen möglich ist. Eine solche Messanordnung profitiert von der erhöhten Empfindlichkeit MOSPR-basierter Biosensoren, hohen Messgeschwindigkeiten und einem verbesserten Signal-Rausch-Verhältnis. Weiterhin wurde der domänenwandassistierte Transport (DOWMAT) superparamagnetischer Partikel über der Oberfläche eines exemplarischen EB-Systems, zur Sensorintegration von Misch-, Reinigungs- und Aufkonzentrationsfunktionen erfolgreich getestet. Die Ergebnisse demonstrieren, dass ein Transport von Partikelreihen mit hohen Geschwindigkeiten bei moderaten externen Magnetfeldern über den entwickelten Schichtsystemen möglich ist. Die Agglomeration der Partikel wird dabei intrinsisch vermieden. Diese Beobachtungen verdeutlichen die Vorzüge des DOWMAT-Mechanismus für biosensorische Anwendungen. Die präsentierten Untersuchungen bilden die Grundlage auf dem Weg zur Umsetzung neuer vielversprechender Biosensorkonzepte, die eine Schlüsselfunktion in der medizinischen point-of-care-Diagnostik bei der Detektion kleinster Konzentrationen krankheitsrelevanter Biomarker einnehmen können.

Alley cropping of willows and grassland for bioenergy provision: productivity, tree-crop interactions and energy balance

The demand for biomass for bioenergy has increased rapidly in industrialized countries in the recent years. Biogenic energy carriers are known to reduce CO2 emissions. However, the resource-inefficient production of biomass often caused negative impacts on the environment, e.g. biodiversity losses, nitrate leaching, and erosion. The detrimental effects evolved mainly from annual crops. Therefore, the aim of modern bioenergy cropping systems is to combine yield stability and environmental benefits by the establishment of mixed-cropping systems. A particular emphasis is on perennial crops which are perceived as environmentally superior to annual crops. Agroforestry systems represent such mixed perennial cropping systems and consist of a mix of trees and arable crops or grassland within the same area of land. Agroforestry practices vary across the globe and alley cropping is a type of agroforestry system which is well adapted to the temperate zone, with a high degree of mechanization. Trees are planted in rows and crops are planted in the alleyways, which facilitates their management by machinery. This study was conducted to examine a young alley cropping system of willows and two grassland mixtures for bioenergy provision under temperate climate conditions. The first part of the thesis identified possible competition effects between willows and the two grassland mixtures. Since light seemed to be the factor most affecting the yield performance of the understory in temperate agroforestry systems, a biennial in situ artificial shade experiment was established over a separate clover-grass stand to quantify the effects of shade. Data to possible below- and aboveground interactions among willows and the two grassland mixtures and their effects on productivity, sward composition, and quality were monitored along a tree-grassland interface within the alleys. In the second part, productivity of the alley cropping system was examined on a triennial time frame and compared to separate grassland and willow stands as controls. Three different conversion technologies (combustion of hay, integrated generation of solid fuel and biogas from biomass, whole crop digestion) were applied to grassland biomass as feedstock and analyzed for its energetic potential. The energetic potential of willow wood chips was calculated by applying combustion as conversion technique. Net energy balances of separate grassland stands, agroforestry and pure willow stands evaluated their energy efficiency. Results of the biennial artificial shade experiment showed that severe shade (80 % light reduction) halved grassland productivity on average compared to a non-shaded control. White clover as heliophilous plant responded sensitively to limited radiation and its dry matter contribution in the sward decreased with increasing shade, whereas non-leguminous forbs (mainly segetal species) benefited. Changes in nutritive quality could not be confirmed by this experiment. Through the study on interactions within the alleys of the young agroforestry system it was possible to outline changes of incident light, soil temperature and sward composition of clover-grass along the tree-grassland interface. Nearly no effects of trees on precipitation, soil moisture and understory productivity occurred along the interface during the biennial experiment. Considering the results of the productivity and the net energy yield alley cropping system had lower than pure grassland stands, irrespective of the grassland seed mixture or fertilization, but was higher than that for pure willow stands. The comparison of three different energetic conversion techniques for the grassland biomass showed highest net energy yields for hay combustion, whereas the integrated generation of solid fuel and biogas from biomass (IFBB) and whole crop digestion performed similarly. However, due to the low fuel quality of hay, its direct combustion cannot be recommended as a viable conversion technique, whereas IFBB fuels were of a similar quality to wood chip from willow.

Parallel Coupled Micro-Macro Actuators

This thesis presents a new actuator system consisting of a micro-actuator and a macro-actuator coupled in parallel via a compliant transmission. The system is called the Parallel Coupled Micro-Macro Actuator, or PaCMMA. In this system, the micro-actuator is capable of high bandwidth force control due to its low mass and direct-drive connection to the output shaft. The compliant transmission of the macro-actuator reduces the impedance (stiffness) at the output shaft and increases the dynamic range of force. Performance improvement over single actuator systems was expected in force control, impedance control, force distortion and reduction of transient impact forces. A set of quantitative measures is proposed and the actuator system is evaluated against them: Force Control Bandwidth, Position Bandwidth, Dynamic Range, Impact Force, Impedance ("Backdriveability'"), Force Distortion and Force Performance Space. Several theoretical performance limits are derived from the saturation limits of the system. A control law is proposed and control system performance is compared to the theoretical limits. A prototype testbed was built using permanenent magnet motors and an experimental comparison was performed between this actuator concept and two single actuator systems. The following performance was observed: Force bandwidth of 56Hz, Torque Dynamic Range of 800:1, Peak Torque of 1040mNm, Minimum Torque of 1.3mNm. Peak Impact Force was reduced by an order of magnitude. Distortion at small amplitudes was reduced substantially. Backdriven impedance was reduced by 2-3 orders of magnitude. This actuator system shows promise for manipulator design as well as psychophysical tests of human performance.

Advanced Nuclear Energy Systems: Heat Transfer Issues and Trends

Almost 450 nuclear power plants are currently operating throughout the world and supplying about 17% of the world’s electricity. These plants perform safely, reliably, and have no free-release of byproducts to the environment. Given the current rate of growth in electricity demand and the ever growing concerns for the environment, the US consumer will favor energy sources that can satisfy the need for electricity and other energy-intensive products (1) on a sustainable basis with minimal environmental impact, (2) with enhanced reliability and safety and (3) competitive economics. Given that advances are made to fully apply the potential benefits of nuclear energy systems, the next generation of nuclear systems can provide a vital part of a long-term, diversified energy supply. The Department of Energy has begun research on such a new generation of nuclear energy systems that can be made available to the market by 2030 or earlier, and that can offer significant advances toward these challenging goals [1]. These future nuclear power systems will require advances in materials, reactor physics as well as heat transfer to realize their full potential. In this paper, a summary of these advanced nuclear power systems is presented along with a short synopsis of the important heat transfer issues. Given the nature of research and the dynamics of these conceptual designs, key aspects of the physics will be provided, with details left for the presentation.

Application for fault location in electrical power distribution systems

Fault location has been studied deeply for transmission lines due to its importance in power systems. Nowadays the problem of fault location on distribution systems is receiving special attention mainly because of the power quality regulations. In this context, this paper presents an application software developed in Matlabtrade that automatically calculates the location of a fault in a distribution power system, starting from voltages and currents measured at the line terminal and the model of the distribution power system data. The application is based on a N-ary tree structure, which is suitable to be used in this application due to the highly branched and the non- homogeneity nature of the distribution systems, and has been developed for single-phase, two-phase, two-phase-to-ground, and three-phase faults. The implemented application is tested by using fault data in a real electrical distribution power system

Necessary and sufficient conditions for robust stability using modal intervals

In this paper, robustness of parametric systems is analyzed using a new approach to interval mathematics called Modal Interval Analysis. Modal Intervals are an interval extension that, instead of classic intervals, recovers some of the properties required by a numerical system. Modal Interval Analysis not only simplifies the computation of interval functions but allows semantic interpretation of their results. Necessary, sufficient and, in some cases, necessary and sufficient conditions for robust performance are presented

Investigación del uso de las tecnologías de información y comunicaciones en la industria logística en Bogotá

Este trabajo de investigación contiene inicialmente una presentación del marco teórico el cual consiste de una breve descripción de la historia de la logística, y del desarrollo de la disciplina de la administración de la cadena de abastecimiento, también denominada gestión de la cadena de suministro. La globalización de los mercados y el incremento de la competencia a nivel mundial, entre otros factores, ha generado varias disciplinas de investigación y desarrollo empresarial bajo la sombrilla de la administración de la cadena de abastecimiento. Dichas disciplinas también se describen brevemente en este trabajo. Luego presentamos una descripción corta de algunas de las tecnologías de la información utilizadas para incrementar la eficiencia en los procesos empresariales. Posteriormente planteamos la investigación del impacto de las tecnologías de la información en empresas del sector logístico en Bogotá, Colombia, que prestan servicios tales como almacenamiento, transporte, intermediación aduanera y operaciones en puerto. Para el desarrollo de dicha investigación, se plantea una encuesta de diez preguntas básicas. Finalmente presentamos los resultados de la investigación, con sus conclusiones y recomendaciones, en donde se evidencia el impacto del tamaño de las empresas y los mercados a los que sirven en la motivación y las barreras para implementar tecnologías de la información en sus procesos y procedimientos.

Plan de mercadeo y logístico para una comercializadora de maquinaría, equipos y artículos para la industria alimenticia

Cormatec Ltda., es una empresa colombiana, dedicada a la comercialización de maquinaria, equipos y artículos para la industria del procesamiento de alimentos, hoteles, restaurantes, carnicerías, frigoríficos y empresas similares. En los últimos años, la empresa ha presentado importantes problemas de disminución de ventas, debido en principio a la fuerte competencia que existe en el sector. Por tal motivo, el presente plan de mercadeo y logístico, busca diagnosticar las causas del bajo rendimiento presentado en la organización en los últimos periodos y proponer soluciones que maximicen las utilidades de la empresa.

Multimedia Systems

These are the materials for the Multimedia Systems course run in ECS. Multimedia Systems is taught rather differently than most courses. Although there is a lecture series, this is to support the main activity - the organisation and participation is a student conference. The coursework is to produce a short paper on a chosen topic to be presented as a paper, poster or demonstration at a course conference to be held at the end of the semester. The process of producing and reviewing the coursework and then participating in the conference has been designed to be the means by students cover the full range of material associated with Multimedia Systems.

Modelación de los sectores estudiados para definir el perfil logístico de Colombia

Colombia siempre ha velado por tener una mejor infraestructura del país, haciendo que se mantenga preocupado por su posición competitiva frente a su desarrollo como hub logístico de Latinoamérica. Esto se ve fundamentado a través de la política nacional logística escrita en el COMPES 3547. Sin embargo, hay un desconocimiento por los empresarios grandes y pequeños del país acerca de las pretensiones que el gobierno quiere llevar a cabo sobre los distintos sectores económicos. La simulación de estructuras como sistemas es de vital importancia para el desarrollo y mejoramiento de cadenas de suministro. La administración de la cadena como sistema que integra procesos permite producir constantemente, mantener niveles adecuados de inventario y cumplir con los requerimientos del cliente final. Lo anterior teniendo en cuenta que los principales actores de la cadena son proveedores, fabricantes, clientes, detallistas, transportadores y distribuidores, En un entorno en el que la globalización constituye quizá el motor más importante para el desempeño de la cadena de suministros, pues rompe barreras geográficas. En síntesis la simulación es un aporte importante para la correcta planeación y operación de la cadena de suministros y esto a la vez permite prestar un buen servicio al cliente mientras se reducen costos y tiempos.

Productividad, innovación y uso de tecnologías de información y las comunicaciones (tic) como factores de desarrollo de la micro, pequeña y mediana empresa (mipyme) en Bogotá.

Las TIC han impactado en el funcionamiento de las organizaciones y han aportado a su proceso evolutivo, generando diversos efectos de acuerdo a la función que estas cumplen dentro de la organización. Las TIC como consecuencia se convierten en una estrategia de gestión en un entorno complejo donde permiten alcanzar mejoras en la organización social, la actividad económica, el bienestar y el acceso a la información y el conocimiento. (Cáceres Carrasco & Aceytuno Pérez, 2008)Con el fin de entender los beneficios de las TIC, se deben brindar a los directores herramientas que permitan formular modelos de negocios efectivos de cara a los mercados y enfocadas a la satisfacción de los clientes. Adicionalmente, para las organizaciones el añadir valor, no sólo hace referencia al servicio que están prestando; hay otros factores diferentes al uso de herramientas TIC y la innovación que también son igual de importantes como: los procesos de apoyo, de gestión que se encuentran de fondo y que hacen posible brindar un servicio al mercado, en estos procesos se encuentran aplicaciones de procedimientos amigables y fáciles de articular, temas como la responsabilidad empresarial, relación y comunicación con competidores dentro del mismo sector, es justamente en las relaciones con los clientes, que las TIC y el uso de Internet puede tener incidencia en los modelos de negocios a través de actividades como el comercio electrónico, el mercadeo electrónico, el mercadeo en línea entre otros. Existen investigaciones acerca de estos temas: innovación, TI, pero no se han establecido relaciones entre ellos, debido a su novedad. Diferentes experiencias laborales de los investigadores en el uso de las TIC como herramienta en la organización de información permiten que surja la idea de llevar a cabo este proyecto abarcando la realidad bogotana de las MiPyme. La presente investigación con un enfoque cualitativo hace una revisión bibliográfica, y bajo la mirada teórica se analiza la relación que tienen los factores de desarrollo que se evidenciaron como son la innovación y el uso de herramientas TIC, como variables dependientes de la productividad de las MiPyme en Bogotá, Colombia, involucrando temas que se relacionan con distintos campos como la tecnología, políticas gubernamentales, y economía.

Definition of an it project portfolio management methodology for a pharmaceutical company

Con la creciente popularidad de las soluciones de IT como factor clave para aumentar la competitividad y la creación de valor para las empresas, la necesidad de invertir en proyectos de IT se incrementa considerablemente. La limitación de los recursos como un obstáculo para invertir ha obligado a las empresas a buscar metodologías para seleccionar y priorizar proyectos, asegurándose de que las decisiones que se toman son aquellas que van alineadas con las estrategias corporativas para asegurar la creación de valor y la maximización de los beneficios. Esta tesis proporciona los fundamentos para la implementación del Portafolio de dirección de Proyectos de IT (IT PPM) como una metodología eficaz para la gestión de proyectos basados en IT, y una herramienta para proporcionar criterios claros para los directores ejecutivos para la toma de decisiones. El documento proporciona la información acerca de cómo implementar el IT PPM en siete pasos, el análisis de los procesos y las funciones necesarias para su ejecución exitosa. Además, proporciona diferentes métodos y criterios para la selección y priorización de proyectos. Después de la parte teórica donde se describe el IT PPM, la tesis aporta un análisis del estudio de caso de una empresa farmacéutica. La empresa ya cuenta con un departamento de gestión de proyectos, pero se encontró la necesidad de implementar el IT PPM debido a su amplia cobertura de procesos End-to-End en Proyectos de IT, y la manera de asegurar la maximización de los beneficios. Con la investigación teórica y el análisis del estudio de caso, la tesis concluye con una definición práctica de un modelo aproximado IT PPM como una recomendación para su implementación en el Departamento de Gestión de Proyectos.

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.