Multifunctions of Bounded Variation, Preliminary Version I

Consider control systems described by a differential equation with a control term or, more generally, by a differential inclusion with velocity set $F(t,x)$. Certain properties of state trajectories can be derived when, in addition to other hypotheses, it is assumed that $F(t,x)$ is merely measurable w.r.t. the time variable $t$. But sometimes a refined analysis requires the imposition of stronger hypotheses regarding the $t$ dependence of $F(t,x)$. Stronger forms of necessary conditions for state trajectories that minimize a cost can derived, for example, if it is hypothesized that $F(t,x)$ is Lipschitz continuous w.r.t. $t$. It has recently become apparent that interesting addition properties of state trajectories can still be derived, when the Lipschitz continuity hypothesis is replaced by the weaker requirement that $F(t,x)$ has bounded variation w.r.t. $t$. This paper introduces a new concept of multifunctions $F(t,x)$ that have bounded variation w.r.t. $t$ near a given state trajectory, of special relevance to control system analysis. Properties of such multifunctions are derived and their significance is illustrated by an application to sensitivity analysis.Comment: Preliminary version of a article which will submitted to a journal for publicatio

Minimax optimal control

Published versio

Measurement Placement in Distribution System State Estimation

Published versio

Conjugate times and regularity of the minimum time function with differential inclusions

This paper studies the regularity of the minimum time function, $T(\cdot)$, for a control system with a general closed target, taking the state equation in the form of a differential inclusion. Our first result is a sensitivity relation which guarantees the propagation of the proximal subdifferential of $T$ along any optimal trajectory. Then, we obtain the local $C^2$ regularity of the minimum time function along optimal trajectories by using such a relation to exclude the presence of conjugate times

Optimal Control Problems with Mixed and Pure State Constraints

This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both “pure” constraints on the state variable and “mixed” constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke's theory of “stratified” necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take into account the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints

(Não) leituras de obras literárias em contexto escolar: um estudo de caso a partir de versão integral e adaptações de "O Cortiço", de Aluísio Azevedo

O presente trabalho se insere nas discussões do grupo de pesquisa Literatura e Educação e investigou, no contexto de uma escola pública de Ensino Fundamental e Médio do município de Guarapari (ES), como são as relações entre livros e leitores - por meio das contribuições teóricas e metodológicas da Nova História Cultural - a partir de três diferentes versões da obra O cortiço do autor Aluísio Azevedo: versão adaptada por Fabio Pinto da coleção É só o começo (2009); adaptação com roteiro de Ivan Jaf e arte de Rodrigo Rosa em história em quadrinhos (2010) distribuída pelo PNBE; e c) versão com texto integral (2014 [1890]); todas encontradas na biblioteca da escola campo. A pesquisa foi desenvolvida em dois momentos, sendo o primeiro de cunho bibliográfico-documental, que buscou perceber como se dão as relações entre livro, leitor e leitura e pensar o modo como algumas adaptações literárias são inseridas no mercado, inclusive as que integram programas de distribuição de livros como o PNBE. O segundo momento foi um estudo de caso com questionário e grupo focal, constituído por alunos de segundo e terceiro ano do Ensino Médio da escola campo, que, no âmbito do processo de educação literária, tentou responder às seguintes questões: a) como se dá a apropriação do texto integral e das diversas adaptações de uma obra pelos estudantes?; b) os textos adaptados despertam no leitor o desejo de conhecer o texto integral?; c) como os alunos agem para (não) realizar as leituras propostas pelo currículo escolar?: A pesquisa justifica-se em face: a) do interesse, nos campos da História e da Literatura, pelas práticas de leitores literários empíricos e pelos usos que são feitos de materiais impressos, em contextos institucionais, em tensão com orientações oficiais; b) da necessidade de se pensar as questões econômico-ideológicas que circundam a leitura em tensionamento com o mercado editorial; c) do nosso diagnóstico tomado aqui como pressuposto de que muitos alunos não leem obras literárias sugeridas pelo currículo escolar; d) da necessidade de se pensar as não leituras literárias para além da culpabilização discente. Com a investigação, conhecemos as formas de aquisição dos livros, algumas preferências, os principais mediadores de leitura, traçando assim um perfil de leitor de leitura literária da escola campo. Chegamos também à conclusão de que algumas adaptações podem ser instrumentos de mediação de leitura em sala de aula. Os autores que nortearam nosso estudo foram: Regina Zilberman (1999, 2013), Márcia Abreu (2001), Edmir Perrotti (1999) e João Wanderlei Geraldi (2010) (livro e leitura no contexto brasileiro); Annie Rouxel (2013), Maria Amélia Dalvi (2012, 2013, 2013a) e Neide Rezende (2013) (educação literária); Roger Chartier (1999, 2002, 2002a, 2010, 2013, 2013a) (práticas e representações, apropriação)

Just-In-Time Compilation of NumPy Vector Operations

In this paper, we introduce JIT compilation for thehigh-productivity framework Python/NumPy in order to boost theperformance significantly. The JIT compilation of Python/NumPyis completely transparent to the user – the runtime system willautomatically JIT compile and execute the NumPy instructionsencountered in a Python application. In other words, we introducea framework that provides the high-productivity from Pythonwhile maintaining the high-performance of a low-level, compiledlanguage.We transforms NumPy vector instruction into an AbstractSyntax Tree representation that creates the basis for furtheroptimizations. From the AST we auto-generate C code whichwe compile into computational kernels and execute. These incorporatetemporary array removal and loop-fusion which are mainbenefactors in the achieved speedups. In order to amortize theoverhead of creation, we also implement a cache for the compiledkernels.We evaluate the JIT compilation by executing several scientificcomputing benchmarks on an AMD. Compared to NumPy, weachieve speedups of a factor 4.72 for a N-Body application and7.51 for a Jacobi Stencil application executing on a single CPUcore

Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem considered on the space of continuously differentiable functions. We approximate the latter with a maximin problem on a finite dimensional subspace of the space of continuously differentiable functions and show that a solution of this problem (existing under natural controllability conditions) can be used for construction of near optimal controls. We illustrate the construction with a numerical example.Comment: 29 pages, 2 figure

An effective mass theorem for the bidimensional electron gas in a strong magnetic field

We study the limiting behavior of a singularly perturbed Schr\"odinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane $(x,y)$ and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr\"odinger equations in the plane $(x,y)$, coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator