Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Probabilistically analysable real-time systems (PROARTIS)

Critical real-time ebedded (CRTE) Systems require safe and tight worst-case execution time (WCET) estimations to provide required safety levels and keep costs low. However, CRTE Systems require increasing performance to satisfy performance needs of existing and new features. Such performance can be only achieved by means of more agressive hardware architectures, which are much harder to analyze from a WCET perspective. The main features considered include cache memòries and multi-core processors.Thus, althoug such features provide higher performance, corrent WCET analysis methods are unable to provide tight WCET estimations. In fact, WCET estimations become worse than for simple rand less powerful hardware. The main reason is the fact that hardware behavior is deterministic but unknown and, therefore, the worst-case behavior must be assumed most of the time, leading to large WCET estimations. The purpose of this project is developing new hardware designs together with WCET analysis tools able to provide tight and safe WCET estimations. In order to do so, those pieces of hardware whose behavior is not easily analyzable due to lack of accurate information during WCET analysis will be enhanced to produce a probabilistically analyzable behavior. Thus, even if the worst-case behavior cannot be removed, its probabilty can be bounded, and hence, a safe and tight WCET can be provided for a particular safety level in line with the safety levels of the remaining components of the system. During the first year the project we have developed molt of the evaluation infraestructure as well as the techniques hardware techniques to analyze cache memories. During the second year those techniques have been evaluated, and new purely-softwar techniques have been developed.

Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Real-time Linux in electric drive systems

Reaaliaikaisten käyttöjärjestelmien käyttö sulautetuissa järjestelmissä on kasvamassa koko ajan. Sulautettuja tietokoneita käytetään yhä useammassa kohteessa kuten sähkökäyttöjen ohjauksessa. Sähkökäyttöjen ohjaus hoidetaan nykyisin yleensä nopealla digitaalisella signaaliprosessorilla (DSP), jolloin ohjelmointi ja päivittäminen on hidasta ja vaikeaa johtuen käytettävästä matalan tason Assembler-kielestä. Ratkaisuna yleiskäyttöisten prosessorien ja reaaliaikakäyttöjärjestelmien käyttö. Kaupalliset reaaliaikakäyttöjärjestelmät ovat kalliita ja lähdekoodin saaminen omaan käyttöön jopa mahdotonta. Linux on ei-kaupallinen avoimen lähdekoodin käyttöjärjestelmä, joten sen käyttö on ilmaista ja sitä voi muokata vapaasti. Linux:iin on saatavana useita laajennuksia, jotka tekevät siitä reaaliaikaisen käyttöjärjestelmän. Vaihtoehtoina joko kova (hard) tai pehmeä (soft) reaaliaikaisuus. Linux:iin on olemassa valmiita kehitysympäristöjä mutta ne kaipaavat parannusta ennen kuin niitä voidaan käyttää suuressa mittakaavassa teollisuudessa. Reaaliaika Linux ei sovellus nopeisiin ohjauslooppeihin (<100 ms) koska nopeus ei riitä vielä mutta nopeus kasvaa samalla kun prosessorit kehittyvät. Linux soveltuu hyvin rajapinnaksi nopean ohjauksen ja käyttäjän välille ja hitaampaan ohjaukseen.

Improving Transportation and Warehousing Efficiency with Simulation-Based Decision Support Systems

Transportation and warehousing are large and growing sectors in the society, and their efficiency is of high importance. Transportation also has a large share of global carbondioxide emissions, which are one the leading causes of anthropogenic climate warming. Various countries have agreed to decrease their carbon emissions according to the Kyoto protocol. Transportation is the only sector where emissions have steadily increased since the 1990s, which highlights the importance of transportation efficiency. The efficiency of transportation and warehousing can be improved with the help of simulations, but models alone are not sufficient. This research concentrates on the use of simulations in decision support systems. Three main simulation approaches are used in logistics: discrete-event simulation, systems dynamics, and agent-based modeling. However, individual simulation approaches have weaknesses of their own. Hybridization (combining two or more approaches) can improve the quality of the models, as it allows using a different method to overcome the weakness of one method. It is important to choose the correct approach (or a combination of approaches) when modeling transportation and warehousing issues. If an inappropriate method is chosen (this can occur if the modeler is proficient in only one approach or the model specification is not conducted thoroughly), the simulation model will have an inaccurate structure, which in turn will lead to misleading results. This issue can further escalate, as the decision-maker may assume that the presented simulation model gives the most useful results available, even though the whole model can be based on a poorly chosen structure. In this research it is argued that simulation- based decision support systems need to take various issues into account to make a functioning decision support system. The actual simulation model can be constructed using any (or multiple) approach, it can be combined with different optimization modules, and there needs to be a proper interface between the model and the user. These issues are presented in a framework, which simulation modelers can use when creating decision support systems. In order for decision-makers to fully benefit from the simulations, the user interface needs to clearly separate the model and the user, but at the same time, the user needs to be able to run the appropriate runs in order to analyze the problems correctly. This study recommends that simulation modelers should start to transfer their tacit knowledge to explicit knowledge. This would greatly benefit the whole simulation community and improve the quality of simulation-based decision support systems as well. More studies should also be conducted by using hybrid models and integrating simulations with Graphical Information Systems.

Pulse response based control for positive definite systems

Pulse Response Based Control (PRBC) is a recently developed minimum time control method for flexible structures. The flexible behavior of the structure is represented through a set of discrete time sequences, which are the responses of the structure due to rectangular force pulses. The rectangular force pulses are given by the actuators that control the structure. The set of pulse responses, desired outputs, and force bounds form a numerical optimization problem. The solution of the optimization problem is a minimum time piecewise constant control sequence for driving the system to a desired final state. The method was developed for driving positive semi-definite systems. In case the system is positive definite, some final states of the system may not be reachable. Necessary conditions for reachability of the final states are derived for systems with a finite number of degrees of freedom. Numerical results are presented that confirm the derived analytical conditions. Numerical simulations of maneuvers of distributed parameter systems have shown a relationship between the error in the estimated minimum control time and sampling interval

Control of Structures with Cubic and Quadratic Non-Linearities with Time Delay Consideration

This paper studies the effect of time delay on the active non-linear control of dynamically loaded flexible structures. The behavior of non-linear systems under state feedback control, considering a fixed time delay for the control force, is investigated. A control method based on non-linear optimal control, using a tensorial formulation and state feedback control is used. The state equations and the control forces are expressed in polynomial form and a performance index, quadratic in both state vector and control forces, is used. General polynomial representations of the non-linear control law are obtained and implemented for control algorithms up to the fifth order. This methodology is applied to systems with quadratic and cubic non-linearities. Strongly non-linear systems are tested and the effectiveness of the control system including a delay for the application of control forces is discussed. Numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. Numerical results emphasize the importance of considering time delay in the project of active structural control systems.

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequent in practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of the sample, thus producing a transfer of mass from some components to other ones, but preserving the total mass present in the system. This evolution is traditionally modelled as a system of ordinary di erential equations of the mass of each component. However, this kind of evolution can be decomposed into a compositional change, expressed in terms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despite of some subcompositions behaving linearly. The goal is to study the characteristics of such simplicial systems of di erential equa- tions such as linearity and stability. This is performed extracting the compositional dif ferential equations from the mass equations. Then, simplicial derivatives are expressed in coordinates of the simplex, thus reducing the problem to the standard theory of systems of di erential equations, including stability. The characterisation of stability of these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and the associated behaviour of the orbits are the main tools. For a three component system, these orbits can be plotted both in coordinates of the simplex or in a ternary diagram. A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is a radioactive decay

Grado de predicción del valor de las acciones ante nuevas emisiones en el sector de extracción de petróleo crudo y gas natural en Colombia, mediante modelos de caos y análisis recurrente

El presente trabajo se enfoca en el análisis de las acciones de Ecopetrol, empresa representativa del mercado de Extracción de Petróleo y Gas natural en Colombia (SP&G), durante el periodo, del 22 de mayo de 2012 al 30 de agosto de 2013. Durante este espacio de tiempo la acción sufrió una serie de variaciones en su precio las cuales se relacionaban a la nueva emisión de acciones que realizo la Compañía. Debido a este cambio en el comportamiento del activo se generaron una serie de interrogantes sobre, (i) la reacción del mercado ante diferentes sucesos ocurridos dentro de las firmas y en su entorno (ii) la capacidad de los modelos financieros de predecir y entender las posibles reacciones observadas de los activos (entendidos como deuda). Durante el desarrollo del presente trabajo se estudiará la pertinencia del mismo, en línea con los objetivos y desarrollos de la Escuela de Administración de la Universidad del Rosario. Puntualmente en temas de Perdurabilidad direccionados a la línea de Gerencia. Donde el entendimiento de la deuda como parte del funcionamiento actual y como variable determinante para el comportamiento futuro de las organizaciones tiene especial importancia. Una vez se clarifica la relación entre el presente trabajo y la Universidad, se desarrollan diferentes conceptos y teorías financieras que han permitido conocer y estudiar de manera más específica el mercado, con el objetivo de reducir los riesgos de las inversiones realizadas. Éste análisis se desarrolla en dos partes: (i) modelos de tiempo discreto y (ii) modelos de tiempo continúo. Una vez se tiene mayor claridad sobre los modelos estudiados hasta el momento se realiza el respectivo análisis de los datos mediante modelos de caos y análisis recurrente los cuales nos permiten entender que las acciones se comportan de manera caótica pero que establecen ciertas relaciones entre los precios actuales y los históricos, desarrollando comportamientos definidos entre los precios, las cantidades, el entorno macroeconómico y la organización. De otra parte, se realiza una descripción del mercado de petróleo en Colombia y se estudia a Ecopetrol como empresa y eje principal del mercado descrito en el país. La compañía Ecopetrol es representativa debido a que es uno de los mayores aportantes fiscales del país, pues sus ingresos se desprenden de bienes que se encuentran en el subsuelo por lo que la renta petrolera incluye impuestos a la producción transformación y consumo (Ecopetrol, 2003). Por último, se presentan los resultados del trabajo, así como el análisis que da lugar para presentar ciertas recomendaciones a partir de lo observado.

Adaptive deadbeat control of stochastic systems

This paper considers the use of a discrete-time deadbeat control action on systems affected by noise. Variations on the standard controller form are discussed and comparisons are made with controllers in which noise rejection is a higher priority objective. Both load and random disturbances are considered in the system description, although the aim of the deadbeat design remains as a tailoring of reference input variations. Finally, the use of such a deadbeat action within a self-tuning control framework is shown to satisfy, under certain conditions, the self-tuning property, generally though only when an extended form of least-squares estimation is incorporated.

Neural networks for linear control: an analysis

This paper considers the use of radial basis function and multi-layer perceptron networks for linear or linearizable, adaptive feedback control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parameterization. A comparison is made with standard, nonneural network algorithms, e.g. self-tuning control.

A dynamical systems framework for intermittent data assimilation

We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.

Regularization of descriptor systems

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.

On relaxed LMI-based designs for fuzzy regulators and fuzzy observers

Relaxed conditions for stability of nonlinear, continuous and discrete-time systems given by fuzzy models are presented. A theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature. Numerical results exemplify this fact. These results are also used for fuzzy regulators and observers designs. The nonlinear systems are represented by fuzzy models proposed by Takagi and Sugeno. The stability analysis and the design of controllers are described by linear matrix inequalities, that can be solved efficiently using convex programming techniques. The specification of the decay rate, constrains on control input and output are also discussed.

Adaptive filter feature identification for structural health monitoring in an aeronautical panel

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)