Algebraic Approach (algebraic + approach)

Distribution by Scientific Domains


Selected Abstracts


A unified algebraic approach to linear control design.

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2003
K.M. Grigoriadis, London 199, R.E. Skelton, T. Iwasaki, Taylor & Francis
No abstract is available for this article. [source]


Iteration domain H, -optimal iterative learning controller design

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2008
Kevin L. Moore
Abstract This paper presents an H, -based design technique for the synthesis of higher-order iterative learning controllers (ILCs) for plants subject to iteration-domain input/output disturbances and plant model uncertainty. Formulating the higher-order ILC problem into a high-dimensional multivariable discrete-time system framework, it is shown how the addition of input/output disturbances and plant model uncertainty to the ILC problem can be cast as an H, -norm minimization problem. The distinctive feature of this formulation is to consider the uncertainty as arising in the iteration domain rather than the time domain. An algebraic approach to solving the problem in this framework is presented, resulting in a sub-optimal controller that can achieve both stability and robust performance. The key observation is that H, synthesis can be used for higher-order ILC design to achieve a reliable performance in the presence of iteration-varying external disturbances and model uncertainty. Copyright © 2007 John Wiley & Sons, Ltd. [source]


Wiener,Kolmogorov Filtering and Smoothing for Multivariate Series With State,Space Structure

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2007
Víctor Gómez
Abstract., Wiener,Kolmogorov filtering and smoothing usually deal with projection problems for stochastic processes that are observed over semi-infinite and doubly infinite intervals. For multivariate stationary series, there exist closed formulae based on covariance generating functions that were first given independently by N. Wiener and A.N. Kolmogorov around 1940. In this article, we consider multivariate series with a state,space structure and, using a new purely algebraic approach to the problem, we prove the equivalence between Wiener,Kolmogorov filtering and Kalman filtering. Up to now, this equivalence has only been partially shown. In addition, we get some new recursions for smoothing and some new recursions to compute the filter weights and the covariance generating functions of the errors. The results are extended to nonstationary series. [source]


The algebraic approach to the phase problem

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2005
A. Cervellino
A rather detailed report is presented on the present status of the algebraic approach to the phase problem in the case of an ideal crystal in order to make clear that some points must still be proven for it to apply to neutron scattering. To make this extension, the most important results that were previously obtained in the case of X-ray scattering are derived again by a different procedure. By so doing, the three-dimensional case is treated explicitly, the polynomial equations in a single variable whose roots determine the positions of the scattering centres are explicitly reported and the procedure is shown to generalize to neutron scattering, overcoming the difficulty related to the non-positivity of the scattering density. In this way, it is fully proven that the atomicity assumption removes the phase ambiguity in the sense that the full diffraction pattern of an ideal crystal can uniquely be reconstructed from a suitable finite portion of it in both X-ray and neutron scattering. The procedures able to isolate these portions that contain the pattern's full information are also given. [source]


Geometrical and algebraic approach to central molecular chirality: A chirality index and an Aufbau description of tetrahedral molecules

CHIRALITY, Issue 7 2006
Salvatore Capozziello
Abstract On the basis of empirical Fischer projections, we develop an algebraic approach to the central molecular chirality of tetrahedral molecules. The elements of such an algebra are obtained from the 24 projections which a single chiral tetrahedron can generate in S and R absolute configurations. They constitute a matrix representation of the O(4) orthogonal group. According to this representation, given a molecule with n chiral centres, it is possible to define an "index of chirality , , {n, p}", where n is the number of stereogenic centres of the molecule and p the number of permutations observed under rotations and superimpositions of the tetrahedral molecule to its mirror image. The chirality index not only assigns the global chirality of a given tetrahedral chain, but indicates also a way to predict the same property for new compounds, which can be built up consistently. Chirality 18:462,468, 2006. © 2006 Wiley-Liss, Inc. [source]


Electrifying diagrams for learning: principles for complex representational systems

COGNITIVE SCIENCE - A MULTIDISCIPLINARY JOURNAL, Issue 6 2002
Peter C.-H.
Abstract Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity,AVOW diagrams (Amps, Volts, Ohms, Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains. [source]