Normas e estabilidade para modelos estocásticos cuja variação do controle e do estado aumentam a incerteza

Orientador: João Bosco Ribeiro do ValDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Essa dissertação de mestrado gira em torno da discussão sobre controle de sistemas incertos. Modelos matemáticos utilizados como base para o design de controladores automáticos são naturalmente uma representação aproximada do sistema real, o que, em conjunto com perturbações externas e dinâmica não modelada, gera incertezas a respeito dos sistemas estudados. Na literatura de controle, este tema vêm sendo discutido frequentemente, em particular nas sub-áreas de controle estocástico e controle robusto. Dentre as técnicas desenvolvidas dentro da teoria de controle estocástico, uma proposta recente se diferencia das demais por basear-se na idéia de que variações abruptas na política de controle possam acarretar em maiores incertezas a respeito do sistema. Matematicamente, essa noção é representada pelo uso de um ruído estocástico dependente do módulo da ação de controle, e a técnica foi apelidada de VCAI - acrônimo para variação do controle aumenta a incerteza. A definição da política de controle ótima correspondente, obtida por meio do método de programação dinâmica, mostra a existência de uma região ao redor do ponto de equilíbrio para a qual a política ótima é manter a ação de controle do equilíbrio inalterada, um resultado que parece particular à abordagem VCAI, mas que pode ser relacionado a políticas de gerenciamento cautelosas em áreas como economia e biologia. O problema de controle ótimo VCAI foi anteriormente resolvido ao adotar-se um critério de custo quadrático descontado e um horizonte de otimização infinito, e nessa dissertação nós utilizamos essa solução para atacar o problema de custo médio a longo prazo. Dada certa semelhança entre a estrutura do ruído estocástico na abordavem VCAI e modelos utilizados na teoria de controle robusto, discutimos ainda possíveis relações entre a abordagem proposta e controladores robustos. Discutimos ainda algumas possíveis aplicações do modelo propostoAbstract: This work discusses a new approach to the control of uncertain systems. Uncertain systems and their representation is a recurrent theme in control theory: approximate mathematical models, unmodeled dynamics and external disturbances are all sources of uncertainties in automated systems, and the topic has been extensively studied in the control literature, particularly within the stochastic and robust control research areas. Within the stochastic framework, a recent approach, named CVIU - control variation increases uncertainty, for short -, was recently proposed. The approach differs from previous models for assuming that a control action might actually increase the uncertainty about an unknown system, a notion represented by the use of stochastic noise depending on the absolute value of the control input. Moreover, the solution of the corresponding stochastic optimal control problem shows the existence of a region around the equilibrium point in which the optimal action is to keep the equilibrium control action unchanged. The CVIU control problem was previously solved by adopting a discounted quadratic cost formulation, and in this work we extend this previous result and study the corresponding long run average control problem. We also discuss possible relations between the CVIU approach and models from robust control theory, and present some potential applications of the theory presented hereMestradoAutomaçãoMestre em Engenharia Elétrica2016/02208-6, 2017/10340-4FAPES

Stochastic analysis of a prey–predator model with herd behaviour of prey

In nature, a number of populations live in groups. As a result when predators attack such a population the interaction occur only at the outer surface of the herd. Again, every model in biology, being concerned with a subsystem of the real world, should include the effect of random fluctuating environment. In this paper, we study a prey–predator model in deterministic and stochastic environment. The social activity of the prey population has been incorporated by using the square root of prey density in the functional response. A brief analysis of the deterministic model including the stability of equilibrium points is presented. In random environment, the birth rate of prey species and death rate of predator species are perturbed by Gaussian white noises. We have used the method of statistical linearization to study the stability and non-equilibrium fluctuation of the populations in stochastic model. Numerical computations carried out to illustrate the analytical findings. The biological implications of analytical and numerical findings are discussed critically

Processing random signals in neuroscience, electrical engineering and operations research

The topic of this dissertation is the study of noise in electrical engineering, neuroscience, biomedical engineering, and operations research through mathematical models that describe, explain, predict and control dynamic phenomena. Noise is modeled through Brownian Motion and the research problems are mathematically addressed by different versions of a generalized Langevin equation. Our mathematical models utilize stochastic differential equations (SDEs) and stochastic optimal control, both of which were born in the soil of electrical engineering. Central to this dissertation is a brain-physics based model of cerebrospinal fluid (CSF) dynamics, whose structure is fundamentally determined by an electrical circuit analogy. Our general Langevin framework encompasses many of the existing equations used in electrical engineering, neuroscience, biomedical engineering and operations research. The generalized SDE for CSF dynamics extends a fundamental model in the field to discover new clinical insights and tools, provides the basis for a nonlinear controller, and suggests a new way to resolve an ongoing controversy regarding CSF dynamics in neuroscience. The natural generalization of the SDE for CSF dynamics is a SDE with polynomial drift. We develop a new analytical algorithm to solve SDEs with polynomial drift, thereby contributing to the electrical engineering literature on signal processing models, many of which are special cases of SDEs with polynomial drift. We make new contributions to the operations research literature on marketing communication models by unifying different types of dynamically optimal trajectories of spending in the framework of a classic model of market response, in which these different temporal patterns arise as a consequence of different boundary conditions. The methodologies developed in this dissertation provide an analytical foundation for the solution of fundamental problems in gas discharge lamp dynamics in power engineering, degradation dynamics of ultra-thin metal oxides in MOS capacitors, and molecular motors in nanotechnology, thereby establishing a rich agenda for future research

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

Comparison of Nonlinear Filtering Methods for Battery State of Charge Estimation

In battery management systems, the main figure of merit is the battery\u27s SOC, typically obtained from voltage and current measurements. Present estimation methods use simplified battery models that do not fully capture the electrical characteristics of the battery, which are useful for system design. This thesis studied SOC estimation for a lithium-ion battery using a nonlinear, electrical-circuit battery model that better describes the electrical characteristics of the battery. The extended Kalman filter, unscented Kalman filter, third-order and fifth-order cubature Kalman filter, and the statistically linearized filter were tested on their ability to estimate the SOC through numerical simulation. Their performances were compared based on their root-mean-square error over one hundred Monte Carlo runs as well as the time they took to complete those runs. The results show that the extended Kalman filter is a good choice for estimating the SOC of a lithium-ion battery