Convex Relaxations of SE(2) and SE(3) for Visual Pose Estimation

This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of $SE(2)$ and $SE(3)$. The approach can use dense point cloud data from stereo vision or an RGB-D sensor (such as the Microsoft Kinect), as well as visual appearance data. The method is a convex relaxation of the classical pose estimation problem, and is based on explicit linear matrix inequality (LMI) representations for the convex hulls of $SE(2)$ and $SE(3)$. Given these representations, the relaxed pose estimation problem can be framed as a robust least squares problem with the optimization variable constrained to these convex sets. Although this formulation is a relaxation of the original problem, numerical experiments indicate that it is indeed exact - i.e. its solution is a member of $SE(2)$ or $SE(3)$ - in many interesting settings. We additionally show that this method is guaranteed to be exact for a large class of pose estimation problems.Comment: ICRA 2014 Preprin

Algebraic observer design for PEM fuel cell system

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, the concept of the algebraic observer is applied to Proton Exchange Membrane Fuel Cell (PEMFC) system. The aim of the proposed observer is to reconstruct the oxygen excess ratio through estimation of their relevant states in real time from the measurement of the supply manifold air pressure. A robust differentiation method is adopted to estimate in finite-time the time derivative of the supply manifold air pressure. Then, the relevant states are reconstructed based on the output-state inversion model. The objective is to minimize the use of extra sensors in order to reduce the costs and enhance the system accuracy. The performance of the proposed observer is analyzed through simulations considering measurement noise and different stack-current variations. The results show that the algebraic observer estimates in finite time and robustly the oxygen-excess ratio.Peer ReviewedPostprint (author's final draft

Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime

A generic PT-symmetric Hamiltonian is assumed tridiagonalized and truncated to N dimensions, and its up-down symmetrized special cases with J=[N/2] real couplings are considered. In the strongly non-Hermitian regime the secular equation gets partially factorized at all N. This enables us to reveal a fine-tuned alignment of the dominant couplings implying an asymptotically sharply spiked shape of the boundary of the J-dimensional quasi-Hermiticity domain in which all the spectrum of energies remains real and observable.Comment: 28 pp., 4 tables, 1 figur

Optimal modelling and experimentation for the improved sustainability of microfluidic chemical technology design

Optimization of the dynamics and control of chemical processes holds the promise of improved sustainability for chemical technology by minimizing resource wastage. Anecdotally, chemical plant may be substantially over designed, say by 35-50%, due to designers taking account of uncertainties by providing greater flexibility. Once the plant is commissioned, techniques of nonlinear dynamics analysis can be used by process systems engineers to recoup some of this overdesign by optimization of the plant operation through tighter control. At the design stage, coupling the experimentation with data assimilation into the model, whilst using the partially informed, semi-empirical model to predict from parametric sensitivity studies which experiments to run should optimally improve the model. This approach has been demonstrated for optimal experimentation, but limited to a differential algebraic model of the process. Typically, such models for online monitoring have been limited to low dimensions. Recently it has been demonstrated that inverse methods such as data assimilation can be applied to PDE systems with algebraic constraints, a substantially more complicated parameter estimation using finite element multiphysics modelling. Parametric sensitivity can be used from such semi-empirical models to predict the optimum placement of sensors to be used to collect data that optimally informs the model for a microfluidic sensor system. This coupled optimum modelling and experiment procedure is ambitious in the scale of the modelling problem, as well as in the scale of the application - a microfluidic device. In general, microfluidic devices are sufficiently easy to fabricate, control, and monitor that they form an ideal platform for developing high dimensional spatio-temporal models for simultaneously coupling with experimentation. As chemical microreactors already promise low raw materials wastage through tight control of reagent contacting, improved design techniques should be able to augment optimal control systems to achieve very low resource wastage. In this paper, we discuss how the paradigm for optimal modelling and experimentation should be developed and foreshadow the exploitation of this methodology for the development of chemical microreactors and microfluidic sensors for online monitoring of chemical processes. Improvement in both of these areas bodes to improve the sustainability of chemical processes through innovative technology. (C) 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved

Stability analysis of a grid-connected VSC controlled by SPC

In the near future a large part of traditional generation based on conventional synchronous machines (SM) will be replaced by renewable generation based on voltage source converters (VSC). In this sense, power system operators have begun to demand VSC-based power plants be able to participate in the frequency and voltage regulation, and are also interested in services like inertia emulation and damping of power oscillation, functions that today are carried out by large synchronous generators. Therefore, several studies have suggested new ways to control voltage source converters, that try to emulate the behavior of synchronous generators and are known generically as Virtual Synchronous Machines. The synchronous power controller (SPC) is a flexible solution that emulates the classical swing equation of a synchronous machine and improves its response. The SPC inherits the advantages of conventional synchronous generators, while it fixes many of its drawbacks. In this work, a sensitivity analysis of a VSC connected to the grid and controlled by SPC is performed. In this sense, a non-linear mathematical model of the system is first developed. This non-linear model is then linearized, obtaining a linear model from which the eigenvalues and sensitivities of the system to some relevant parameters are calculated. Finally, time-domain simulations are performed to confirm the results of the sensitivity analysis.Postprint (author's final draft

Backpropagation training in adaptive quantum networks

We introduce a robust, error-tolerant adaptive training algorithm for generalized learning paradigms in high-dimensional superposed quantum networks, or \emph{adaptive quantum networks}. The formalized procedure applies standard backpropagation training across a coherent ensemble of discrete topological configurations of individual neural networks, each of which is formally merged into appropriate linear superposition within a predefined, decoherence-free subspace. Quantum parallelism facilitates simultaneous training and revision of the system within this coherent state space, resulting in accelerated convergence to a stable network attractor under consequent iteration of the implemented backpropagation algorithm. Parallel evolution of linear superposed networks incorporating backpropagation training provides quantitative, numerical indications for optimization of both single-neuron activation functions and optimal reconfiguration of whole-network quantum structure.Comment: Talk presented at "Quantum Structures - 2008", Gdansk, Polan