Incremental Control Synthesis for Robotics in the Presence of Temporal Logic Specifications

This thesis presents methods for incrementally constructing controllers in the presence of uncertainty and nonlinear dynamics. The basic setting is motion planning subject to temporal logic specifications. Broadly, two categories of problems are treated. The first is reactive formal synthesis when so-called discrete abstractions are available. The fragment of linear-time temporal logic (LTL) known as GR(1) is used to express assumptions about an adversarial environment and requirements of the controller. Two problems of changes to a specification are posed that concern the two major aspects of GR(1): safety and liveness. Algorithms providing incremental updates to strategies are presented as solutions. In support of these, an annotation of strategies is developed that facilitates repeated modifications. A variety of properties are proven about it, including necessity of existence and sufficiency for a strategy to be winning. The second category of problems considered is non-reactive (open-loop) synthesis in the absence of a discrete abstraction. Instead, the presented stochastic optimization methods directly construct a control input sequence that achieves low cost and satisfies a LTL formula. Several relaxations are considered as heuristics to address the rarity of sampling trajectories that satisfy an LTL formula and demonstrated to improve convergence rates for Dubins car and single-integrators subject to a recurrence task.

Estimation of catalyst activity profiles and deactivation parameters from reactor operating data with applications to naphtha reforming

Techniques are developed for estimating activity profiles in fixed bed reactors and catalyst deactivation parameters from operating reactor data. These techniques are applicable, in general, to most industrial catalytic processes. The catalytic reforming of naphthas is taken as a broad example to illustrate the estimation schemes and to signify the physical meaning of the kinetic parameters of the estimation equations. The work is described in two parts. Part I deals with the modeling of kinetic rate expressions and the derivation of the working equations for estimation. Part II concentrates on developing various estimation techniques.

Part I: The reactions used to describe naphtha reforming are dehydrogenation and dehydroisomerization of cycloparaffins; isomerization, dehydrocyclization and hydrocracking of paraffins; and the catalyst deactivation reactions, namely coking on alumina sites and sintering of platinum crystallites. The rate expressions for the above reactions are formulated, and the effects of transport limitations on the overall reaction rates are discussed in the appendices. Moreover, various types of interaction between the metallic and acidic active centers of reforming catalysts are discussed as characterizing the different types of reforming reactions.

Part II: In catalytic reactor operation, the activity distribution along the reactor determines the kinetics of the main reaction and is needed for predicting the effect of changes in the feed state and the operating conditions on the reactor output. In the case of a monofunctional catalyst and of bifunctional catalysts in limiting conditions, the cumulative activity is sufficient for predicting steady reactor output. The estimation of this cumulative activity can be carried out easily from measurements at the reactor exit. For a general bifunctional catalytic system, the detailed activity distribution is needed for describing the reactor operation, and some approximation must be made to obtain practicable estimation schemes. This is accomplished by parametrization techniques using measurements at a few points along the reactor. Such parametrization techniques are illustrated numerically with a simplified model of naphtha reforming.

To determine long term catalyst utilization and regeneration policies, it is necessary to estimate catalyst deactivation parameters from the the current operating data. For a first order deactivation model with a monofunctional catalyst or with a bifunctional catalyst in special limiting circumstances, analytical techniques are presented to transform the partial differential equations to ordinary differential equations which admit more feasible estimation schemes. Numerical examples include the catalytic oxidation of butene to butadiene and a simplified model of naphtha reforming. For a general bifunctional system or in the case of a monofunctional catalyst subject to general power law deactivation, the estimation can only be accomplished approximately. The basic feature of an appropriate estimation scheme involves approximating the activity profile by certain polynomials and then estimating the deactivation parameters from the integrated form of the deactivation equation by regression techniques. Different bifunctional systems must be treated by different estimation algorithms, which are illustrated by several cases of naphtha reforming with different feed or catalyst composition.

Approximate analytical description for fundamental-mode fields of graded-index fibers: Beyond the Gaussian approximation

An approximate analytical description for fundamental-mode fields of graded-index fibers is explicitly presented by use of the power-series expansion method, the maximum-value condition at the fiber axis, the decay properties of fundamental-mode fields at large distance from the fiber axis, and the approximate modal parameters U obtained from the Gaussian approximation. This analytical description is much more accurate than the Gaussian approximation and at the same time keep the simplicity of the latter. As two special examples, we present the approximate analytical formulas for the fundamental-mode fields of a step profile fiber and a Gaussian profile fiber, and we find that they are both highly accurate in the single-mode range by comparing them with the corresponding exact solutions.

Corrections to the paraxial approximation of an arbitrary free-propagation beam

A relatively simple transform from an arbitrary solution of the paraxial wave equation to the corresponding exact solution of the Helmholtz wave equation is derived in the condition that the evanescent waves are ignored and is used to study the corrections to the paraxial approximation of an arbitrary free-propagation beam. Specifically, the general lowest-order correction field is given in a very simple form and is proved to be exactly consistent with the perturbation method developed by Lax et nl. [Phys. Rev. A 11, 1365 (1975)]. Some special examples, such as the lowest-order correction to the paraxial approximation of a fundamental Gaussian beam whose waist plane has a parallel shin from the z = 0 plane, are presented. (C) 1998 Optical Society of America.

Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media

The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].

Phase unwrapping algorithms, respectively, based on path-following and discrete cosine transform

This paper describes a path-following phase unwrapping algorithm and a phase unwrapping algorithm based on discrete cosine transform (DCT) which accelerates the Computation and suppresses the propagation of noise. Through analysis of fringe pattern with serious noises simulated in mathematic model, we make a contrast between path-following algorithm and DCT algorithm. The advantages and disadvantages or analytical fringe pattern are also given through comparison of two algorithms. Three-dimensional experimental results have been given to prove the validity of these algorithms. Despite DCT phase unwrapping technique robustness and speed in some cases, it cannot be unwrapping inconsistencies phase. The path-following algorithm can be used in automation analysis of fringe patterns with little influence of noise. (c) 2007 Elsevier GmbH. All rights reserved.

Application of Entropy and Fractal Dimension Analyses to the Pattern Recognition of Contaminated Fish Responses in Aquaculture

The objective of the work was to develop a non-invasive methodology for image acquisition, processing and nonlinear trajectory analysis of the collective fish response to a stochastic event. Object detection and motion estimation were performed by an optical flow algorithm in order to detect moving fish and simultaneously eliminate background, noise and artifacts. The Entropy and the Fractal Dimension (FD) of the trajectory followed by the centroids of the groups of fish were calculated using Shannon and permutation Entropy and the Katz, Higuchi and Katz-Castiglioni's FD algorithms respectively. The methodology was tested on three case groups of European sea bass (Dicentrarchus labrax), two of which were similar (C1 control and C2 tagged fish) and very different from the third (C3, tagged fish submerged in methylmercury contaminated water). The results indicate that Shannon entropy and Katz-Castiglioni were the most sensitive algorithms and proved to be promising tools for the non-invasive identification and quantification of differences in fish responses. In conclusion, we believe that this methodology has the potential to be embedded in online/real time architecture for contaminant monitoring programs in the aquaculture industry.

Algoritmos multi-objetivos para la optimización de una secuencia de matrices generadoras en computación cuántica topológica

Quantum Computing is a relatively modern field which simulates quantum computation conditions. Moreover, it can be used to estimate which quasiparticles would endure better in a quantum environment. Topological Quantum Computing (TQC) is an approximation for reducing the quantum decoherence problem1, which is responsible for error appearance in the representation of information. This project tackles specific instances of TQC problems using MOEAs (Multi-objective Optimization Evolutionary Algorithms). A MOEA is a type of algorithm which will optimize two or more objectives of a problem simultaneously, using a population based approach. We have implemented MOEAs that use probabilistic procedures found in EDAs (Estimation of Distribution Algorithms), since in general, EDAs have found better solutions than ordinary EAs (Evolutionary Algorithms), even though they are more costly. Both, EDAs and MOEAs are population-based algorithms. The objective of this project was to use a multi-objective approach in order to find good solutions for several instances of a TQC problem. In particular, the objectives considered in the project were the error approximation and the length of a solution. The tool we used to solve the instances of the problem was the multi-objective framework PISA. Because PISA has not too much documentation available, we had to go through a process of reverse-engineering of the framework to understand its modules and the way they communicate with each other. Once its functioning was understood, we began working on a module dedicated to the braid problem. Finally, we submitted this module to an exhaustive experimentation phase and collected results.

Contributions on distance-based algorithms, multi-classifier construction and pairwise classification

179 p.