On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification

We present a new approach to convexification of the Tikhonov regularization using a continuation method strategy. We embed the original minimization problem into a one-parameter family of minimization problems. Both the penalty term and the minimizer of the Tikhonov functional become dependent on a continuation parameter. In this way we can independently treat two main roles of the regularization term, which are stabilization of the ill-posed problem and introduction of the a priori knowledge. For zero continuation parameter we solve a relaxed regularization problem, which stabilizes the ill-posed problem in a weaker sense. The problem is recast to the original minimization by the continuation method and so the a priori knowledge is enforced. We apply this approach in the context of topology-to-shape geometry identification, where it allows to avoid the convergence of gradient-based methods to a local minima. We present illustrative results for magnetic induction tomography which is an example of PDE constrained inverse problem

Proportional-Integral-Plus Control Strategy of an Intelligent Excavator

This article considers the application of Proportional-Integral-Plus (PIP) control to the Lancaster University Computerised Intelligent Excavator (LUCIE), which is being developed to dig foundation trenches on a building site. Previous work using LUCIE was based on the ubiquitous PI/PID control algorithm, tuned on-line, and implemented in a rather ad hoc manner. By contrast, the present research utilizes new hardware and advanced model-based control system design methods to improve the joint control and so provide smoother, more accurate movement of the excavator arm. In this article, a novel nonlinear simulation model of the system is developed for MATLAB/SIMULINK, allowing for straightforward refinement of the control algorithm and initial evaluation. The PIP controller is compared with a conventionally tuned PID algorithm, with the final designs implemented on-line for the control of dipper angle. The simulated responses and preliminary implementation results demonstrate the feasibility of the approach

Optimal Control and Spatial Heterogeneity: Pattern Formation in Economic-Ecological Models

This paper extends Turing analysis to standard recursive optimal control frameworks in economics and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics under optimal control over space creates (or destroys) spatial heterogeneity. We show how our approach reduces the analysis to a tractable extension of linearization methods applied to the spatial analog of the well known costate/state dynamics. We explicitly show the existence of a non-empty Turing space of diffusive instability by developing a linear-quadratic approximation of the original non-linear problem. We apply our method to a bioeconomic problem, but the method has more general economic applications where spatial considerations and pattern formation are important. We believe that the extension of Turing analysis and the theory associated with the dispersion relationship to recursive infinite horizon optimal control settings is new.Spatial analysis, Pattern formation, Turing mechanism, Turing space, Pontryagin’s principle, Bioeconomics

Métodos de controle modal tolerante a danos para estruturas flexíveis

Orientadores: Eurípedes Guilherme de Oliveira Nóbrega, Nazih Mechbal, Gérard Maurice Henri CoffignalTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Estruturas inteligentes estão cada vez mais presentes em diferentes aplicações na indústria, em particular nas áreas de aeronáutica e engenharia civil. Essas estruturas possuem características que permitem interações com o ambiente, adaptando suas propriedades de acordo com as necessidades (rigidez, amortecimento, viscosidade, etc.), monitorando a própria saúde estrutural (SHM, de Structural Health Monitoring) ou controlando suas vibrações. Atualmente, os métodos ativos para controle de vibrações não respondem adequadamente a mudanças na dinâmica estrutural causada por dano, apesar da boa capacidade de rejeição a perturbações externas. O controle ativo tolerante a danos (DTAC, de Damage-Tolerant Active Control) é uma área recente de pesquisa que objetiva desenvolver métodos integrados para reduzir vibrações e, ao mesmo tempo, monitorar a integridade estrutural, sendo possível identificar a ocorrência de danos e, com isso, reconfigurar o controlador ativo de vibrações. Esta tese contribui com a área de DTAC propondo uma nova abordagem de controle modal e algumas estratégias de aplicações. Os métodos propostos focam no controle de vibrações de estruturas flexíveis sujeitas a danos com múltiplos sensores e atuadores não colocados. Os capítulos apresentam quatro temas principais e as conclusões. O Capítulo 2 revisa o problema subótimo H? e sua respectiva solução por meio da abordagem por desigualdades matriciais lineares, que é uma ferramenta fundamental para o desenvolvimento dos tópicos subsequentes. O Capítulo 3 introduz o método de controle modal de vibrações baseado na norma H? modal, a qual revela elevada seletividade modal, permitindo a concentração de energia de controle sobre os efeitos do dano e apresentando robustez em relação ao spillover e à variação paramétrica. Uma nova estratégia de controle é desenvolvida no Capítulo 4, tendo em conta o conhecimento existente sobre as regiões da estrutura com alta probabilidade de sofrer danos, o que leva a requisitos específicos no projeto do controlador H? modal. Uma técnica de SHM é usada para avaliar o efeito do dano em cada modo, dado que é usado para projetar um controlador preventivo. O Capítulo 5 apresenta uma metodologia modal de dupla malha que lida com a imprevisibilidade do dano, garantindo um bom compromisso entre robustez e desempenho para a estrutura saudável ou danificada. Para atingir esse objetivo, o controlador modal da primeira malha é projetado para atender os requisitos de desempenho para a estrutura saudável. O controlador da segunda malha é reconfigurado objetivando assegurar robustez e um desempenho satisfatório quando, ou se, um dano ocorre. Essa lei de controle é baseada em um observador de estados e em um algoritmo de SHM para reconfigurar o controlador online. Todas as técnicas propostas são testadas utilizando estruturas inteligentes criadas a partir de simulações (analíticas e de elementos finitos) e/ou experimentos. O último capítulo discute os principais resultados obtidos para cada abordagem descrita nos capítulos anterioresAbstract: Smart structures have increasingly become present in different industry applications and particularly in the fields of aeronautics and civil engineering. These structures have features that allow interactions with the environment, adapting their characteristics according to the needs (stiffness, damping, viscosity, etc.), monitoring their health or controlling their vibrations. Today, smart structure active control methods do not respond appropriately to damage, despite the capability of good rejection of external disturbances. Damage-tolerant active control (DTAC) is a recent research area that aims to develop integrated approaches to reduce vibrations while monitoring the structure integrity, identifying damage occurrence and reconfiguring the control law of the adopted active vibration control method. This thesis contributes to the DTAC area by proposing a novel modal control framework and some application strategies. The developed methods focus on noncollocated flexible structures, where multiple piezoelectric sensors and actuators are used to attenuate damaged structure vibration. The chapters present four main topics and the conclusions. Chapter 2 reviews the regular suboptimal H? problem and its respective solution based on the linear matrix inequality approach, which is a fundamental tool for the development of subsequent topics. Chapter 3 introduces the modal H?-norm-based method for vibration control, which reveals high modal selectivity, allowing control energy concentration on damage effects and presenting robustness to spillover and parameter variation. A new control strategy is developed in Chapter 4, taking into account existing knowledge about the structure stressed regions with high probability of damage occurrence, leading to specific requirements in the modal H?-controller design. A structural health monitoring (SHM) technique assesses each damaged mode behavior, which is used to design a preventive controller. Chapter 5 presents a novel modal double-loop control methodology to deal with the unpredictability of damage, nevertheless ensuring a good compromise between robustness and performance to both healthy and damaged structures. For this purpose, the first-loop modal controller is designed to comply with regular requirements for the healthy structure behavior and the second-loop controller is reconfigured aiming to ensure satisfactory performance and robustness when and if damage occurs, based on a state observer and an SHM technique to adapt the controller online. In all these chapters, simulated (analytical- and finite-element-based) and/or experimental smart structures are used to examine the proposed methodology under the respective control strategies. The last chapter summarises the achieved results for each different approach described in the previous chaptersDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânica141621/2012-512337/13-7CNPQCAPE

Improved Wind Turbine Control Strategies for Maximizing Power Output and Minimizing Power Flicker

For reducing the cost of energy (COE) for wind power, controls techniques are important for enhancing energy yield, reducing structural load and improving power quality. This thesis presents the control strategies studies for wind turbine both from the perspectives of both maximizing power output and reducing power flicker and structural load, First, a self-optimizing robust control scheme is developed with the objective of maximizing the power output of a variable speed wind turbine with doubly-fed induction generator (DFIG) operated in Region 2. Wind power generation can be divided into two stages: conversion from aerodynamic power to rotor (mechanical) power and conversion from rotor power to the electrical (grid) power. In this work, the maximization of power generation is achieved by a two-loop control structure in which the power control for each stage has intrinsic synergy. The outer loop is an Extremum Seeking Control (ESC) based generator torque regulation via the rotor power feedback. The ESC can search for the optimal torque constant to maximize the rotor power without wind measurement or accurate knowledge of power map. The inner loop is a vector-control based scheme that can both regulate the generator torque requested by the ESC and also maximize the conversion from the rotor power to grid power. In particular, an ∞ controller is synthesized for maximizing, with performance specifications defined based upon the spectrum of the rotor power obtained by the ESC. Also, the controller is designed to be robust against the variations of some generator parameters. The proposed control strategy is validated via simulation study based on the synergy of several software packages including the TurbSim and FAST developed by NREL, Simulink and SimPowerSystems. Then, a bumpless transfer scheme is proposed for inter-region controller switching scheme in order to reduce the power fluctuation and structural load under fluctuating wind conditions. This study considers the division of Region 2, Region 2.5 and Region 3 in the neighborhood of the rated wind speed. When wind, varies around the rated wind speed, the switching of control can lead to significant fluctuation in power and voltage supply, as well as structural loading. To smooth the switch and improve the tracking, two different bumpless transfer methods, Conditioning and Linear Quadratic techniques, are employed for different inter-region switching situations. The conditioning bumpless transfer approach adopted for switching between Region 2 maximum power capture controls to Region 2.5 rotor speed regulation via generator torque. For the switch between Region 2.5 and Region 3, the generator torque windup at rated value and pitch controller become online to limit the load of wind turbine. LQ technique is posed to reduce the discontinuity at the switch between torque controller and pitch controller by using an extra compensator. The flicker emission of the turbine during the switching is calculated to evaluate power fluctuation. The simulation results demonstrated the effectiveness of the proposed scheme of inter-region switching, with significant reduction of power flicker as well as the damage equivalent load

Renormalization of radiobiological response functions by energy loss fluctuations and complexities in chromosome aberration induction: deactivation theory for proton therapy from cells to tumor control

We employ a multi-scale mechanistic approach to investigate radiation induced cell toxicities and deactivation mechanisms as a function of linear energy transfer in hadron therapy. Our theoretical model consists of a system of Markov chains in microscopic and macroscopic spatio-temporal landscapes, i.e., stochastic birth-death processes of cells in millimeter-scale colonies that incorporates a coarse-grained driving force to account for microscopic radiation induced damage. The coupling, hence the driving force in this process, stems from a nano-meter scale radiation induced DNA damage that incorporates the enzymatic end-joining repair and mis-repair mechanisms. We use this model for global fitting of the high-throughput and high accuracy clonogenic cell-survival data acquired under exposure of the therapeutic scanned proton beams, the experimental design that considers $\gamma$-H2AX as the biological endpoint and exhibits maximum observed achievable dose and LET, beyond which the majority of the cells undergo collective biological deactivation processes. An estimate to optimal dose and LET calculated from tumor control probability by extension to $~ 10^6$ cells per $mm$-size voxels is presented. We attribute the increase in degree of complexity in chromosome aberration to variabilities in the observed biological responses as the beam linear energy transfer (LET) increases, and verify consistency of the predicted cell death probability with the in-vitro cell survival assay of approximately 100 non-small cell lung cancer (NSCLC) cells

Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge

We propose a linear-quadratic (LQ) control problem of streamflow discharge by optimizing an infinite-dimensional jump-driven stochastic differential equation (SDE). Our SDE is a superposition of Ornstein-Uhlenbeck processes (supOU process), generating a sub-exponential autocorrelation function observed in actual data. The integral operator Riccati equation is heuristically derived to determine the optimal control of the infinite-dimensional system. In addition, its finite-dimensional version is derived with a discretized distribution of the reversion speed and computed by a finite difference scheme. The optimality of the Riccati equation is analyzed by a verification argument. The supOU process is parameterized based on the actual data of a perennial river. The convergence of the numerical scheme is analyzed through computational experiments. Finally, we demonstrate the application of the proposed model to realistic problems along with the Kolmogorov backward equation for the performance evaluation of controls

Modeling Persistent Trends in Distributions

We present a nonparametric framework to model a short sequence of probability distributions that vary both due to underlying effects of sequential progression and confounding noise. To distinguish between these two types of variation and estimate the sequential-progression effects, our approach leverages an assumption that these effects follow a persistent trend. This work is motivated by the recent rise of single-cell RNA-sequencing experiments over a brief time course, which aim to identify genes relevant to the progression of a particular biological process across diverse cell populations. While classical statistical tools focus on scalar-response regression or order-agnostic differences between distributions, it is desirable in this setting to consider both the full distributions as well as the structure imposed by their ordering. We introduce a new regression model for ordinal covariates where responses are univariate distributions and the underlying relationship reflects consistent changes in the distributions over increasing levels of the covariate. This concept is formalized as a "trend" in distributions, which we define as an evolution that is linear under the Wasserstein metric. Implemented via a fast alternating projections algorithm, our method exhibits numerous strengths in simulations and analyses of single-cell gene expression data.Comment: To appear in: Journal of the American Statistical Associatio