VHDL-based system design of a cognitive sensorimotor loop (CSL) for haptic Human-Machine Interaction (HMI)

This document is a summary of the Bachelor thesis titled “VHDL-Based System Design of a Cognitive Sensorimotor Loop (CSL) for Haptic Human-Machine Interaction (HMI)” written by Pablo de Miguel Morales, Electronics Engineering student at the Universidad Politécnica de Madrid (UPM Madrid, Spain) during an Erasmus+ Exchange Program at the Beuth Hochschule für Technik (BHT Berlin, Germany). The tutor of this project is Dr. Prof. Hild. This project has been developed inside the Neurobotics Research Laboratory (NRL) in close collaboration with Benjamin Panreck, a member of the NRL, and another exchange student from the UPM Pablo Gabriel Lezcano. For a deeper comprehension of the content of the thesis, a deeper look in the document is needed as well as the viewing of the videos and the VHDL design. In the growing field of automation, a large amount of workforce is dedicated to improve, adapt and design motor controllers for a wide variety of applications. In the specific field of robotics or other machinery designed to interact with humans or their environment, new needs and technological solutions are often being discovered due to the existing, relatively unexplored new scenario it is. The project consisted of three main parts: Two VHDL-based systems and one short experiment on the haptic perception. Both VHDL systems are based on a Cognitive Sensorimotor Loop (CSL) which is a control loop designed by the NRL and mainly developed by Dr. Prof. Hild. The CSL is a control loop whose main characteristic is the fact that it does not use any external sensor to measure the speed or position of the motor but the motor itself. The motor always generates a voltage that is proportional to its angular speed so it does not need calibration. This method is energy efficient and simplifies control loops in complex systems. The first system, named CSL Stay In Touch (SIT), consists in a one DC motor system controller by a FPGA Board (Zynq ZYBO 7000) whose aim is to keep contact with any external object that touches its Sensing Platform in both directions. Apart from the main behavior, three features (Search Mode, Inertia Mode and Return Mode) have been designed to enhance the haptic interaction experience. Additionally, a VGA-Screen is also controlled by the FPGA Board for the monitoring of the whole system. This system has been completely developed, tested and improved; analyzing its timing and consumption properties. The second system, named CSL Fingerlike Mechanism (FM), consists in a fingerlike mechanical system controlled by two DC motors (Each controlling one part of the finger). The behavior is similar to the first system but in a more complex structure. This system was optional and not part of the original objectives of the thesis and it could not be properly finished and tested due to the lack of time. The haptic perception experiment was an experiment conducted to have an insight into the complexity of human haptic perception in order to implement this knowledge into technological applications. The experiment consisted in testing the capability of the subjects to recognize different objects and shapes while being blindfolded and with their ears covered. Two groups were done, one had full haptic perception while the other had to explore the environment with a plastic piece attached to their finger to create a haptic handicap. The conclusion of the thesis was that a haptic system based only on a CSL-based system is not enough to retrieve valuable information from the environment and that other sensors are needed (temperature, pressure, etc.) but that a CSL-based system is very useful to control the force applied by the system to interact with haptic sensible surfaces such as skin or tactile screens. RESUMEN. Este documento es un resumen del proyecto fin de grado titulado “VHDL-Based System Design of a Cognitive Sensorimotor Loop (CSL) for Haptic Human-Machine Interaction (HMI)” escrito por Pablo de Miguel, estudiante de Ingeniería Electrónica de Comunicaciones en la Universidad Politécnica de Madrid (UPM Madrid, España) durante un programa de intercambio Erasmus+ en la Beuth Hochschule für Technik (BHT Berlin, Alemania). El tutor de este proyecto ha sido Dr. Prof. Hild. Este proyecto se ha desarrollado dentro del Neurorobotics Research Laboratory (NRL) en estrecha colaboración con Benjamin Panreck (un miembro del NRL) y con Pablo Lezcano (Otro estudiante de intercambio de la UPM). Para una comprensión completa del trabajo es necesaria una lectura detenida de todo el documento y el visionado de los videos y análisis del diseño VHDL incluidos en el CD adjunto. En el creciente sector de la automatización, una gran cantidad de esfuerzo está dedicada a mejorar, adaptar y diseñar controladores de motor para un gran rango de aplicaciones. En el campo específico de la robótica u otra maquinaria diseñada para interactuar con los humanos o con su entorno, nuevas necesidades y soluciones tecnológicas se siguen desarrollado debido al relativamente inexplorado y nuevo escenario que supone. El proyecto consta de tres partes principales: Dos sistemas basados en VHDL y un pequeño experimento sobre la percepción háptica. Ambos sistemas VHDL están basados en el Cognitive Sesnorimotor Loop (CSL) que es un lazo de control creado por el NRL y cuyo desarrollador principal ha sido Dr. Prof. Hild. El CSL es un lazo de control cuya principal característica es la ausencia de sensores externos para medir la velocidad o la posición del motor, usando el propio motor como sensor. El motor siempre genera un voltaje proporcional a su velocidad angular de modo que no es necesaria calibración. Este método es eficiente en términos energéticos y simplifica los lazos de control en sistemas complejos. El primer sistema, llamado CSL Stay In Touch (SIT), consiste en un sistema formado por un motor DC controlado por una FPGA Board (Zynq ZYBO 7000) cuyo objetivo es mantener contacto con cualquier objeto externo que toque su plataforma sensible en ambas direcciones. Aparte del funcionamiento básico, tres modos (Search Mode, Inertia Mode y Return Mode) han sido diseñados para mejorar la interacción. Adicionalmente, se ha diseñado el control a través de la FPGA Board de una pantalla VGA para la monitorización de todo el sistema. El sistema ha sido totalmente desarrollado, testeado y mejorado; analizando su propiedades de timing y consumo energético. El segundo sistema, llamado CSL Fingerlike Mechanism (FM), consiste en un mecanismo similar a un dedo controlado por dos motores DC (Cada uno controlando una falange). Su comportamiento es similar al del primer sistema pero con una estructura más compleja. Este sistema no formaba parte de los objetivos iniciales del proyecto y por lo tanto era opcional. No pudo ser plenamente desarrollado debido a la falta de tiempo. El experimento de percepción háptica fue diseñado para profundizar en la percepción háptica humana con el objetivo de aplicar este conocimiento en aplicaciones tecnológicas. El experimento consistía en testear la capacidad de los sujetos para reconocer diferentes objetos, formas y texturas en condiciones de privación del sentido del oído y la vista. Se crearon dos grupos, en uno los sujetos tenían plena percepción háptica mientras que en el otro debían interactuar con los objetos a través de una pieza de plástico para generar un hándicap háptico. La conclusión del proyecto fue que un sistema háptico basado solo en sistemas CSL no es suficiente para recopilar información valiosa del entorno y que debe hacer uso de otros sensores (temperatura, presión, etc.). En cambio, un sistema basado en CSL es idóneo para el control de la fuerza aplicada por el sistema durante la interacción con superficies hápticas sensibles tales como la piel o pantallas táctiles.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

Poster presented in the 24th European Symposium on Computer Aided Process Engineering (ESCAPE 24), Budapest, Hungary, June 15-18, 2014.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

In this work, we analyze the effect of incorporating life cycle inventory (LCI) uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear programming (MILP) coupled with a two-step transformation scenario generation algorithm with the unique feature of providing scenarios where the LCI random variables are correlated and each one of them has the desired lognormal marginal distribution. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study of a petrochemical supply chain. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact, and moreover the correlation among environmental burdens provides more realistic scenarios for the decision making process.

Visioni di una utopia moderna : l'immagine della città nelle rappresentazione delle smart cities e il ruolo del design per construire scenari di mondi futuro

Le nostre città stanno cambiando profondamente in relazione ad alcuni fenomeni urbani: la crescita della popolazione, i cambiamenti climatici e la scarsità di risorse energetiche stanno modificando lo stile di vita e la forma delle città. E' necessario modificare alcuni preconcetti per concepire, costruire e vivere in un modo nuovo lo spazio urbano; questo processo prende il nome di Smart City. Per realizzare una Smart City è necessaria una visione olistica dei processi e dei fenomeni urbani; designer e urbanisti devono lavorare insieme per visualizzare gli scenari della città del futuro, tenendo conto delle possibilità offerte dalla tecnologia. Il design della comunicazione ha il compito di creare queste visioni, comunicando le idee di città del futuro e interpretando il ruolo di mediatore, per rendere comprensibili i linguaggi delle molteplici discipline. Questa ricerca ha l'obiettivo di realizzare uno strumento destinato ai designer che elaborano gli scenari del futuro, e agli attori del contesto urbano che interpretano quelle visioni, per pianificare efficaci strategie di miglioramento.

Putting Up a Big Front: Car Design and Size Affect Road-Crossing Behaviour

Previous research suggests that people tend to see faces in car fronts and that they attribute personality characteristics to car faces. In the present study we investigated whether car design influences pedestrian road-crossing behaviour. An immersive virtual reality environment with a zebra crossing scenario was used to determine a) whether the minimum accepted distance for crossing the street is larger for cars with a dominant appearance than for cars with a friendly appearance and b) whether the speed of dominant-looking cars is overestimated as compared to friendly-looking cars. Participants completed both tasks while either standing on the pavement or on the centre island. We found that people started to cross the road later in front of friendly-looking low-power cars compared to dominant-looking high-power cars, but only if the cars were relatively large in size. For small cars we found no effect of power. The speed of smaller cars was estimated to be higher compared to large cars (size-speed bias). Furthermore, there was an effect of starting position: From the centre island, participants entered the road significantly later (i. e. closer to the approaching car) and left the road later than when starting from the pavement. Similarly, the speed of the cars was estimated significantly lower when standing on the centre island compared to the pavement. To our knowledge, this is the first study to show that car fronts elicit responses on a behavioural level.

Design and development of logistics workflow systems for demand management with RFID

This paper discusses demand and supply chain management and examines how artificial intelligence techniques and RFID technology can enhance the responsiveness of the logistics workflow. This proposed system is expected to have a significant impact on the performance of logistics networks by virtue of its capabilities to adapt unexpected supply and demand changes in the volatile marketplace with the unique feature of responsiveness with the advanced technology, Radio Frequency Identification (RFID). Recent studies have found that RFID and artificial intelligence techniques drive the development of total solution in logistics industry. Apart from tracking the movement of the goods, RFID is able to play an important role to reflect the inventory level of various distribution areas. In today’s globalized industrial environment, the physical logistics operations and the associated flow of information are the essential elements for companies to realize an efficient logistics workflow scenario. Basically, a flexible logistics workflow, which is characterized by its fast responsiveness in dealing with customer requirements through the integration of various value chain activities, is fundamental to leverage business performance of enterprises. The significance of this research is the demonstration of the synergy of using a combination of advanced technologies to form an integrated system that helps achieve lean and agile logistics workflow.

The effects of sex of teacher, sex of scenario principal, and leadership style on the performance ratings of scenario principals by teachers

This study was designed to address questions regarding the effects of sex and leadership style on teacher perceptions of principal effectiveness. On a researcher-designed instrument, middle school teachers rated the effectiveness of a scenario principal's response in several situations. The responses reflected varying levels of Task and Relationship Behavior.^ The design incorporated two between subjects factors (Teacher Sex and Principal Sex) and one within subjects factor (Leadership Style) which was treated as a repeated measure. An analysis of variance revealed no significant effects except for Leadership Style. Overall, High Task/High Relationship behavior rated significantly higher and Low Task/Low Relationship rated significantly lower than the others. The null hypothesis concerning differences could not be rejected and the stated research hypotheses were not supported.^ Additional analyses of variance were conducted substituting subject demographic variables for Teacher Sex in the research design. No significant interactions or main effects other than Leadership Style were noted when either Age or Ethnicity were substituted.^ A significant two-way interaction was noted for Teacher Experience and Leadership Style (p =.0316). Less experienced teachers rated principal's performance lower when exhibiting High Task/Low Relationship style than did more experienced teachers. A significant three-way interaction was noted for Administrative Aspiration x Principal Sex x Leadership Style (p =.0294). Teachers who indicated an intent to enter administration differed more on their ratings between male and female principals exhibiting mixed styles of High Task/Low Relationship and Low Task/High Relationship than did teachers who indicated no or undecided.^ Sex of the teacher appears less important than sex of the principal on performance ratings. Results suggest further study of the effects of teacher experience and teacher administrative aspiration on perceptions of principal effectiveness. ^

Design of a dynamic e-commerce system with engineering applications

The primary purpose of this thesis was to design and develop a prototype e-commerce system where dynamic parameters are included in the decision-making process and execution of an online transaction. The system developed and implemented takes into account previous usage history, priority and associated engineering capabilities. The system was developed using three-tiered client server architecture. The interface was the Internet browser. The middle tiered web server was implemented using Active Server Pages, which form a link between the client system and other servers. A relational database management system formed the data component of the three-tiered architecture. It includes a capability for data warehousing which extracts needed information from the stored data of the customers as well as their orders. The system organizes and analyzes the data that is generated during a transaction to formulate a client's behavior model during and after a transaction. This is used for making decisions like pricing, order rescheduling during a client's forthcoming transaction. The system helps among other things to bring about predictability to a transaction execution process, which could be highly desirable in the current competitive scenario.

The effects of sex of teacher, sex of scenario principal and leadership style on the performance ratings of scenario principals by teachers

This study was designed to address questions regarding the effects of sex and leadership style on teacher perceptions of principal effectiveness. On a researcher-designed instrument, middle school teachers rated the effectiveness of a scenario principal's response in several situations. The responses reflected varying levels of Task and Relationship Behavior. The design incorporated two between subjects factors (Teacher Sex and Principal Sex) and one within subjects factor (Leadership Style) which was treated as a repeated measure. An analysis of variance revealed no significant effects except for Leadership Style. Overall, High Task/High Relationship behavior rated significantly higher and Low Task/Low Relationship rated significantly lower than the others. The null hypothesis concerning differences could not be rejected and the stated research hypotheses were not supported. Additional analyses of variance were conducted substituting subject demographic variables for Teacher Sex in the research design. No significant interactions or main effects other than Leadership Style were noted when either Age or Ethnicity were substituted. A significant two-way interaction was noted for Teacher Experience and Leadership Style (p = .0316). Less experienced teachers rated principal's performance lower when exhibiting High Task/Low Relationship style than did more experienced teachers. A significant three-way interaction was noted for Administrative Aspiration x Principal Sex x Leadership Style (p = .0294). Teachers who indicated an intent to enter administration differed more on their ratings between male and female principals exhibiting mixed styles of High Task/Low Relationship and Low Task/High Relationship than did teachers who indicated no or undecided. Sex of the teacher appears less important than sex of the principal on performance ratings. Results suggest further study of the effects of teacher experience and teacher administrative aspiration on perceptions of principal effectiveness.

Design and implementation of a relative localization system for ground and aerial robotic teams

The main focus of this thesis is to address the relative localization problem of a heterogenous team which comprises of both ground and micro aerial vehicle robots. This team configuration allows to combine the advantages of increased accessibility and better perspective provided by aerial robots with the higher computational and sensory resources provided by the ground agents, to realize a cooperative multi robotic system suitable for hostile autonomous missions. However, in such a scenario, the strict constraints in flight time, sensor pay load, and computational capability of micro aerial vehicles limits the practical applicability of popular map-based localization schemes for GPS denied navigation. Therefore, the resource limited aerial platforms of this team demand simpler localization means for autonomous navigation. Relative localization is the process of estimating the formation of a robot team using the acquired inter-robot relative measurements. This allows the team members to know their relative formation even without a global localization reference, such as GPS or a map. Thus a typical robot team would benefit from a relative localization service since it would allow the team to implement formation control, collision avoidance, and supervisory control tasks, independent of a global localization service. More importantly, a heterogenous team such as ground robots and computationally constrained aerial vehicles would benefit from a relative localization service since it provides the crucial localization information required for autonomous operation of the weaker agents. This enables less capable robots to assume supportive roles and contribute to the more powerful robots executing the mission. Hence this study proposes a relative localization-based approach for ground and micro aerial vehicle cooperation, and develops inter-robot measurement, filtering, and distributed computing modules, necessary to realize the system. The research study results in three significant contributions. First, the work designs and validates a novel inter-robot relative measurement hardware solution which has accuracy, range, and scalability characteristics, necessary for relative localization. Second, the research work performs an analysis and design of a novel nonlinear filtering method, which allows the implementation of relative localization modules and attitude reference filters on low cost devices with optimal tuning parameters. Third, this work designs and validates a novel distributed relative localization approach, which harnesses the distributed computing capability of the team to minimize communication requirements, achieve consistent estimation, and enable efficient data correspondence within the network. The work validates the complete relative localization-based system through multiple indoor experiments and numerical simulations. The relative localization based navigation concept with its sensing, filtering, and distributed computing methods introduced in this thesis complements system limitations of a ground and micro aerial vehicle team, and also targets hostile environmental conditions. Thus the work constitutes an essential step towards realizing autonomous navigation of heterogenous teams in real world applications.

Integrating functional connectivity and climate change in the design of protected area networks

Le rapide déclin actuel de la biodiversité est inquiétant et les activités humaines en sont la cause directe. De nombreuses aires protégées ont été mises en place pour contrer cette perte de biodiversité. Afin de maximiser leur efficacité, l’amélioration de la connectivité fonctionnelle entre elles est requise. Les changements climatiques perturbent actuellement les conditions environnementales de façon globale. C’est une menace pour la biodiversité qui n’a pas souvent été intégrée lors de la mise en place des aires protégées, jusqu’à récemment. Le mouvement des espèces, et donc la connectivité fonctionnelle du paysage, est impacté par les changements climatiques et des études ont montré qu’améliorer la connectivité fonctionnelle entre les aires protégées aiderait les espèces à faire face aux impacts des changements climatiques. Ma thèse présente une méthode pour concevoir des réseaux d’aires protégées tout en tenant compte des changements climatiques et de la connectivité fonctionnelle. Mon aire d’étude est la région de la Gaspésie au Québec (Canada). La population en voie de disparition de caribou de la Gaspésie-Atlantique (Rangifer tarandus caribou) a été utilisée comme espèce focale pour définir la connectivité fonctionnelle. Cette petite population subit un déclin continu dû à la prédation et la modification de son habitat, et les changements climatiques pourraient devenir une menace supplémentaire. J’ai d’abord construit un modèle individu-centré spatialement explicite pour expliquer et simuler le mouvement du caribou. J’ai utilisé les données VHF éparses de la population de caribou et une stratégie de modélisation patron-orienté pour paramétrer et sélectionner la meilleure hypothèse de mouvement. Mon meilleur modèle a reproduit la plupart des patrons de mouvement définis avec les données observées. Ce modèle fournit une meilleure compréhension des moteurs du mouvement du caribou de la Gaspésie-Atlantique, ainsi qu’une estimation spatiale de son utilisation du paysage dans la région. J’ai conclu que les données éparses étaient suffisantes pour ajuster un modèle individu-centré lorsqu’utilisé avec une modélisation patron-orienté. Ensuite, j’ai estimé l’impact des changements climatiques et de différentes actions de conservation sur le potentiel de mouvement du caribou. J’ai utilisé le modèle individu-centré pour simuler le mouvement du caribou dans des paysages hypothétiques représentant différents scénarios de changements climatiques et d’actions de conservation. Les actions de conservation représentaient la mise en place de nouvelles aires protégées en Gaspésie, comme définies par le scénario proposé par le gouvernement du Québec, ainsi que la restauration de routes secondaires à l’intérieur des aires protégées. Les impacts des changements climatiques sur la végétation, comme définis dans mes scénarios, ont réduit le potentiel de mouvement du caribou. La restauration des routes était capable d’atténuer ces effets négatifs, contrairement à la mise en place des nouvelles aires protégées. Enfin, j’ai présenté une méthode pour concevoir des réseaux d’aires protégées efficaces et j’ai proposé des nouvelles aires protégées à mettre en place en Gaspésie afin de protéger la biodiversité sur le long terme. J’ai créé de nombreux scénarios de réseaux d’aires protégées en étendant le réseau actuel pour protéger 12% du territoire. J’ai calculé la représentativité écologique et deux mesures de connectivité fonctionnelle sur le long terme pour chaque réseau. Les mesures de connectivité fonctionnelle représentaient l’accès général aux aires protégées pour le caribou de la Gaspésie-Atlantique ainsi que son potentiel de mouvement à l’intérieur. J’ai utilisé les estimations de potentiel de mouvement pour la période de temps actuelle ainsi que pour le futur sous différents scénarios de changements climatiques pour représenter la connectivité fonctionnelle sur le long terme. Le réseau d’aires protégées que j’ai proposé était le scénario qui maximisait le compromis entre les trois caractéristiques de réseau calculées. Dans cette thèse, j’ai expliqué et prédit le mouvement du caribou de la Gaspésie-Atlantique sous différentes conditions environnementales, notamment des paysages impactés par les changements climatiques. Ces résultats m’ont aidée à définir un réseau d’aires protégées à mettre en place en Gaspésie pour protéger le caribou au cours du temps. Je crois que cette thèse apporte de nouvelles connaissances sur le comportement de mouvement du caribou de la Gaspésie-Atlantique, ainsi que sur les actions de conservation qui peuvent être prises en Gaspésie afin d’améliorer la protection du caribou et de celle d’autres espèces. Je crois que la méthode présentée peut être applicable à d’autres écosystèmes aux caractéristiques et besoins similaires.

Mission and Scenario Planning for Unmanned Aerial Vehicles (Path Planning and Collision Avoidance Systems)

As unmanned autonomous vehicles (UAVs) are being widely utilized in military and civil applications, concerns are growing about mission safety and how to integrate dierent phases of mission design. One important barrier to a coste ective and timely safety certication process for UAVs is the lack of a systematic approach for bridging the gap between understanding high-level commander/pilot intent and implementation of intent through low-level UAV behaviors. In this thesis we demonstrate an entire systems design process for a representative UAV mission, beginning from an operational concept and requirements and ending with a simulation framework for segments of the mission design, such as path planning and decision making in collision avoidance. In this thesis, we divided this complex system into sub-systems; path planning, collision detection and collision avoidance. We then developed software modules for each sub-system

Minimum-order filter design for partial state estimation of linear systems with multiple time-varying state delays and unknown input delays

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.