An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems

This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the data from an array of sensors forms the forcing function. The solution of the equation is formulated as a least squares (LS) problem with linear constraints. The LS approach makes the method suitable for the explicit solution of inverse problems where the forcing function is perturbed by noise. The algebraic computation is partitioned into a initial preparatory step, which precomputes the matrices required for the run-time computation; and the cyclic run-time computation, which is repeated with each acquisition of sensor data. The cyclic computation consists of a single matrix-vector multiplication, in this manner computation complexity is known a-priori, fulfilling the definition of a real-time computation. Numerical testing of the new method is presented on perturbed as well as unperturbed problems; the results are compared with known analytic solutions and solutions acquired from state-of-the-art implicit solvers. The solution is implemented with model based design and uses only fundamental linear algebra; consequently, this approach supports automatic code generation for deployment on embedded systems. The targeting concept was tested via software- and processor-in-the-loop verification on two systems with different processor architectures. Finally, the method was tested on a laboratory prototype with real measurement data for the monitoring of flexible structures. The problem solved is: the real-time overconstrained reconstruction of a curve from measured gradients. Such systems are commonly encountered in the monitoring of structures and/or ground subsidence.Comment: 24 pages, journal articl

Polynomial Invariants for Affine Programs

We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose assignments are given by affine expressions). Our main tool is an algebraic result of independent interest: given a finite set of rational square matrices of the same dimension, we show how to compute the Zariski closure of the semigroup that they generate

Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K

We consider systems A_\ell(t) y(q^\ell t) + ... + A_0(t) y(t) = b(t) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.Comment: 8 page

Design of an Integrated SDN/NFV management and orchestration architecture

This project aims at explaining and defining the SDN technology with integration of the NFV technology. We will also see the logic of this technology applied to a program designed for this project. The objective of this project is to understand the purpose of this technology, where is it going to be used, why companies like Google or Microsoft for over 2 years have been investing time and resources to develop and to implement the technology on the corporate level, as well as on the level of regular user like you and me. Firstly we will focus on the explanation of the SDN technology, what it is, what for is it going to be used and what is the future of this technology. Why the SDN is so important? Next, we will explain the use of the NFV and show how it is going to change the way we see the network right now. NFV also works with the SDN. Once we define the basics of the two technologies, we will proceed to the explanation of the practical part of this project. I would like to comment on the software used for this project is open source, since the OS used on the machine that carried out the simulations, and wrote this lines, to the package Rstudio. The practical part is to simulate how will work the network flows when this technology is used. The program will optimize the resources that we want for the proper performance of the global system. For example, we can optimize the path, the number of machines the flow has to cross, optimize the global delay of the flow, etc. Finally, we will reach specific conclusions based on the work we have done, as well as some personal outcome, such as the analysis of the difficulties encountered during the performance, as well as training and finally knowledge gained through work

Computationally Efficient Simulation of Queues: The R Package queuecomputer

Large networks of queueing systems model important real-world systems such as MapReduce clusters, web-servers, hospitals, call centers and airport passenger terminals. To model such systems accurately, we must infer queueing parameters from data. Unfortunately, for many queueing networks there is no clear way to proceed with parameter inference from data. Approximate Bayesian computation could offer a straightforward way to infer parameters for such networks if we could simulate data quickly enough. We present a computationally efficient method for simulating from a very general set of queueing networks with the R package queuecomputer. Remarkable speedups of more than 2 orders of magnitude are observed relative to the popular DES packages simmer and simpy. We replicate output from these packages to validate the package. The package is modular and integrates well with the popular R package dplyr. Complex queueing networks with tandem, parallel and fork/join topologies can easily be built with these two packages together. We show how to use this package with two examples: a call center and an airport terminal.Comment: Updated for queuecomputer_0.8.

New Perspectives on Modelling and Control for Next Generation Intelligent Transport Systems

This PhD thesis contains 3 major application areas all within an Intelligent Transportation System context. The first problem we discuss considers models that make beneficial use of the large amounts of data generated in the context of traffic systems. We use a Markov chain model to do this, where important data can be taken into account in an aggregate form. The Markovian model is simple and allows for fast computation, even on low end computers, while at the same time allowing meaningful insight into a variety of traffic system related issues. This allows us to both model and enable the control of aggregate, macroscopic features of traffic networks. We then discuss three application areas for this model: the modelling of congestion, emissions, and the dissipation of energy in electric vehicles. The second problem we discuss is the control of pollution emissions in eets of hybrid vehicles. We consider parallel hybrids that have two power units, an internal combustion engine and an electric motor. We propose a scheme in which we can in uence the mix of the two engines in each car based on simple broadcast signals from a central infrastructure. The infrastructure monitors pollution levels and can thus make the vehicles react to its changes. This leads to a context aware system that can be used to avoid pollution peaks, yet does not restrict drivers unnecessarily. In this context we also discuss technical constraints that have to be taken into account in the design of traffic control algorithms that are of a microscopic nature, i.e. they affect the operation of individual vehicles. We also investigate ideas on decentralised trading of emissions. The goal here is to allocate the rights to pollute fairly among the eet's vehicles. Lastly we discuss the usage of decentralised stochastic assignment strategies in traffic applications. Systems are considered in which reservation schemes can not reliably be provided or enforced and there is a signifficant delay between decisions and their effect. In particular, our approach facilitates taking into account the feedback induced into traffic systems by providing forecasts to large groups of users. This feedback can invalidate the predictions if not modelled carefully. At the same time our proposed strategies are simple rules that are easy to follow, easy to accept, and significantly improve the performance of the systems under study. We apply this approach to three application areas, the assignment of electric vehicles to charging stations, the assignment of vehicles to parking facilities, and the assignment of customers to bike sharing stations. All discussed approaches are analysed using mathematical tools and validated through extensive simulations