Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.

The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times

This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE).

Reliability evaluation of distribution systems considering automatic reclosers

This paper presents a new methodology to evaluate in a predictive way the reliability of distribution systems, considering the impact of automatic recloser switches. The developed algorithm is based on state enumeration techniques with Markovian models and on the minimal cut set theory. Some computational aspects related with the implementation of the proposed algorithm in typical distribution networks are also discussed. The description of the proposed approach is carried out using a sample test system. The results obtained with a typical configuration of a Brazilian system (EDP Bandeirante Energia S.A.) are presented and discussed.

A synthetic control chart for monitoring the process mean and variance

Purpose - The aim of this paper is to present a synthetic chart based on the non-central chi-square statistic that is operationally simpler and more effective than the joint X̄ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes. Design/methodology/approach - The approach used is based on the non-central chi-square statistic and the steady-state average run length (ARL) of the developed chart is evaluated using a Markov chain model. Findings - The proposed chart always detects process disturbances faster than the joint X̄ and R charts. The developed chart can monitor the process instead of looking at two charts separately. Originality/value - The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately. © Emerald Group Publishing Limted.

On the determination of epsilon during discriminative GMM training

Discriminative training of Gaussian Mixture Models (GMMs) for speech or speaker recognition purposes is usually based on the gradient descent method, in which the iteration step-size, ε, uses to be defined experimentally. In this letter, we derive an equation to adaptively determine ε, by showing that the second-order Newton-Raphson iterative method to find roots of equations is equivalent to the gradient descent algorithm. © 2010 IEEE.

Reactive power support pricing of distributed generators with primary energy source uncertainty

In this paper, a novel methodology to price the reactive power support ancillary service of Distributed Generators (DGs) with primary energy source uncertainty is shown. The proposed methodology provides the service pricing based on the Loss of Opportunity Costs (LOC) calculation. An algorithm is proposed to reduce the uncertainty present in these generators using Multiobjective Power Flows (MOPFs) implemented in multiple probabilistic scenarios through Monte Carlo Simulations (MCS), and modeling the time series associated with the generation of active power from DGs through Markov Chains (MC). © 2011 IEEE.

Pricing of reactive power support provided by distributed generators in transmission systems

Distributed Generation, microgrid technologies, two-way communication systems, and demand response programs are issues that are being studied in recent years within the concept of smart grids. At some level of enough penetration, the Distributed Generators (DGs) can provide benefits for sub-transmission and transmission systems through the so-called ancillary services. This work is focused on the ancillary service of reactive power support provided by DGs, specifically Wind Turbine Generators (WTGs), with high level of impact on transmission systems. The main objective of this work is to propose an optimization methodology to price this service by determining the costs in which a DG incurs when it loses sales opportunity of active power, i.e, by determining the Loss of Opportunity Costs (LOC). LOC occur when more reactive power is required than available, and the active power generation has to be reduced in order to increase the reactive power capacity. In the optimization process, three objectives are considered: active power generation costs of DGs, voltage stability margin of the system, and losses in the lines of the network. Uncertainties of WTGs are reduced solving multi-objective optimal power flows in multiple probabilistic scenarios constructed by Monte Carlo simulations, and modeling the time series associated with the active power generation of each WTG via Fuzzy Logic and Markov Chains. The proposed methodology was tested using the IEEE 14 bus test system with two WTGs installed. © 2011 IEEE.

Distributed generators as providers of reactive power support - A market approach

Traditionally, ancillary services are supplied by large conventional generators. However, with the huge penetration of distributed generators (DGs) as a result of the growing interest in satisfying energy requirements, and considering the benefits that they can bring along to the electrical system and to the environment, it appears reasonable to assume that ancillary services could also be provided by DGs in an economical and efficient way. In this paper, a settlement procedure for a reactive power market for DGs in distribution systems is proposed. Attention is directed to wind turbines connected to the network through synchronous generators with permanent magnets and doubly-fed induction generators. The generation uncertainty of this kind of DG is reduced by running a multi-objective optimization algorithm in multiple probabilistic scenarios through the Monte Carlo method and by representing the active power generated by the DGs through Markov models. The objectives to be minimized are the payments of the distribution system operator to the DGs for reactive power, the curtailment of transactions committed in an active power market previously settled, the losses in the lines of the network, and a voltage profile index. The proposed methodology was tested using a modified IEEE 37-bus distribution test system. © 1969-2012 IEEE.

Aspectos de avaliação de desempenho em redes ponto a ponto e ponto multiponto baseados em modelagem Markoviana e medições

Esta tese apresenta uma metodologia para avaliação de desempenho de redes de acesso banda larga. A avaliação de desempenho de redes é uma forma de identificar e analisar como determinadas características tais como diferentes tipos de tráfego ou formas de utilização, por exemplo, podem influenciar no comportamento da rede em foco, podendo assim prever como tal rede se comportará frente a situações futuras. A metodologia apresentada é composta de duas abordagens: uma abordagem baseada em medições e outra baseada em modelagem via processos Markovianos. As redes analisadas englobam os dois tipos básicos de arquitetura de acesso: redes ADSL2+ (linha digital do assinante assimétrica 2+ – Asymmetric Digital Subscriber Line 2+), as quais são redes cabeadas que utilizam cabos metálicos de pares trançados; redes FBWN (rede sem fio banda larga fixa – Fixed Broadband Wireless Network), as quais são redes sem fio (wireless) baseadas no padrão IEEE 802.16. A abordagem de medições é focada na forma como a rede analisada se comporta frente a três situações: transmissão de um tráfego genérico; impacto de ruídos não-estacionários no sistema; e uso da rede como meio de transmissão de tráfego multimídia em tempo real. A abordagem de modelagem, por sua vez, ´e baseada em prever o comportamento das redes analisadas utilizando uma formulação matemática fundamentada em processos Markovianos. Os resultados apresentados indicam a viabilidade de aplicação desta metodologia como forma de avaliação de desempenho. Os resultados ainda tornam possível a extensão desta metodologia a outros tipos de redes de acesso banda larga, tais como: redes de fibras ópticas, redes de enlaces de microondas, redes VDSL/VDSL2 (linha digital do assinante de alta taxa de dados – Very-high-data-rate DSL), etc.

Charakterisierung und Konvergenz mehrdimensionaler kontinuierlicher Verzweigungsprozesse

In dieser Arbeit wird eine Klasse von stochastischen Prozessen untersucht, die eine abstrakte Verzweigungseigenschaft besitzen. Die betrachteten Prozesse sind homogene Markov-Prozesse in stetiger Zeit mit Zuständen im mehrdimensionalen reellen Raum und dessen Ein-Punkt-Kompaktifizierung. Ausgehend von Minimalforderungen an die zugehörige Übergangsfunktion wird eine vollständige Charakterisierung der endlichdimensionalen Verteilungen mehrdimensionaler kontinuierlicher Verzweigungsprozesse vorgenommen. Mit Hilfe eines erweiterten Laplace-Kalküls wird gezeigt, dass jeder solche Prozess durch eine bestimmte spektral positive unendlich teilbare Verteilung eindeutig bestimmt ist. Umgekehrt wird nachgewiesen, dass zu jeder solchen unendlich teilbaren Verteilung ein zugehöriger Verzweigungsprozess konstruiert werden kann. Mit Hilfe der allgemeinen Theorie Markovscher Operatorhalbgruppen wird sichergestellt, dass jeder mehrdimensionale kontinuierliche Verzweigungsprozess eine Version mit Pfaden im Raum der cadlag-Funktionen besitzt. Ferner kann die (funktionale) schwache Konvergenz der Prozesse auf die vage Konvergenz der zugehörigen Charakterisierungen zurückgeführt werden. Hieraus folgen allgemeine Approximations- und Konvergenzsätze für die betrachtete Klasse von Prozessen. Diese allgemeinen Resultate werden auf die Unterklasse der sich verzweigenden Diffusionen angewendet. Es wird gezeigt, dass für diese Prozesse stets eine Version mit stetigen Pfaden existiert. Schließlich wird die allgemeinste Form der Fellerschen Diffusionsapproximation für mehrtypige Galton-Watson-Prozesse bewiesen.

Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.

Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Forecasting cost based on a stochastic utilization plan and a fixed cost function

The application of Markov processes is very useful to health-care problems. The objective of this study is to provide a structured methodology of forecasting cost based upon combining a stochastic model of utilization (Markov Chain) and deterministic cost function. The perspective of the cost in this study is the reimbursement for the services rendered. The data to be used is the OneCare database of claim records of their enrollees over a two-year period of January 1, 1996–December 31, 1997. The model combines a Markov Chain that describes the utilization pattern and its variability where the use of resources by risk groups (age, gender, and diagnosis) will be considered in the process and a cost function determined from a fixed schedule based on real costs or charges for those in the OneCare claims database. The cost function is a secondary application to the model. Goodness-of-fit will be used checked for the model against the traditional method of cost forecasting. ^

Modelos baseados em agentes aplicados à dinâmica de preços do mercado imobiliário

Um dos aspectos regulatórios fundamentais para o mercado imobiliário no Brasil são os limites para obtenção de financiamento no Sistema Financeiro de Habitação. Esses limites podem ser definidos de forma a aumentar ou reduzir a oferta de crédito neste mercado, alterando o comportamento dos seus agentes e, com isso, o preço de mercado dos imóveis. Neste trabalho, propomos um modelo de formação de preços no mercado imobiliário brasileiro com base no comportamento dos agentes que o compõem. Os agentes vendedores têm comportamento heterogêneo e são influenciados pela demanda histórica, enquanto que os agentes compradores têm o seu comportamento determinado pela disponibilidade de crédito. Esta disponibilidade de crédito, por sua vez, é definida pelos limites para concessão de financiamento no Sistema Financeiro de Habitação. Verificamos que o processo markoviano que descreve preço de mercado converge para um sistema dinâmico determinístico quando o número de agentes aumenta, e analisamos o comportamento deste sistema dinâmico. Mostramos qual é a família de variáveis aleatórias que representa o comportamento dos agentes vendedores de forma que o sistema apresente um preço de equilíbrio não trivial, condizente com a realidade. Verificamos ainda que o preço de equilíbrio depende não só das regras de concessão de financiamento no Sistema Financeiro de Habitação, como também do preço de reserva dos compradores e da memória e da sensibilidade dos vendedores a alterações na demanda. A memória e a sensibilidade dos vendedores podem levar a oscilações de preços acima ou abaixo do preço de equilíbrio (típicas de processos de formação de bolhas); ou até mesmo a uma bifurcação de Neimark-Sacker, quando o sistema apresenta dinâmica oscilatória estável.