607 research outputs found
Determination of division algebras with 243 elements
Finite nonassociative division algebras (i.e., finite semifields) with 243
elements are completely classified.Comment: 6 pages, 3 table
Consistency of objective Bayes factors as the model dimension grows
In the class of normal regression models with a finite number of regressors,
and for a wide class of prior distributions, a Bayesian model selection
procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer.
Statist. Assoc. 104 (2009) 1261--1271]. However, in models where the number of
parameters increases as the sample size increases, properties of the Bayes
factor are not totally understood. Here we study consistency of the Bayes
factors for nested normal linear models when the number of regressors increases
with the sample size. We pay attention to two successful tools for model
selection [Schwarz Ann. Statist. 6 (1978) 461--464] approximation to the Bayes
factor, and the Bayes factor for intrinsic priors [Berger and Pericchi J. Amer.
Statist. Assoc. 91 (1996) 109--122, Moreno, Bertolino and Racugno J. Amer.
Statist. Assoc. 93 (1998) 1451--1460]. We find that the the Schwarz
approximation and the Bayes factor for intrinsic priors are consistent when the
rate of growth of the dimension of the bigger model is for . When
the Schwarz approximation is always inconsistent under the alternative
while the Bayes factor for intrinsic priors is consistent except for a small
set of alternative models which is characterized.Comment: Published in at http://dx.doi.org/10.1214/09-AOS754 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Dead-Time compensators: A unified approach
IFAC Linear Time Delay Systems,Grenoble,France,1998This paper shows how most dead-time compensators can be considered as a particular case ofa proposed general control structure. The proposed structure can be tuned taking into account the performance and robustness ofthe closed-loop. The obtained controller is more general and allows better results than previous algorithms. In order to illustrate the results, some simulation examples are shown
Prediction for control
5th IFAC Conference on System Structure and Control 1998 (SSC'98), Nantes, France, 8-10 JulyThis paper shows that "optimal" controllers based on "optimal" predictor structures are not "optimal" in their closed loop behaviour and that predictors should be designed taking into account closed-loop considerations. This is first illustrated with a first order plant with delay. The ISE index is computed for two typical optimal controllers (minimum variance controller and generalized predictive controller) when a stochastic disturbance is considered. The results are compared to those obtained by the use of a non optimal PI controller that uses a non optimal Smith predictor and performs better than the optimal controllers for the illustrative example. A general structure for predictors is proposed. In order to illustrate the results, some simulation examples are shown.Ce papier montre que des lois de commandes "optimales" basees sur des structures predictives "optimales" ne sont pas "optimales" dans leur comportement en boucle fermee et que la synthese de predicteurs devrait prendre en compte des considerations de boucle fermee. Cela est d'abord illustre avec un systeme du premier ordre a retard. l'index ISE est calcule pour deux lois de commandes optimales typiques (loi de commande a variance minim ale et loi de commande predictive generalisee), quand une perturbation stochastique est consideree. Les resultats sont compares a. ceux obtenus avec un regulateur PI non optimal base sur un predicteur de Smith non optimal et sont, pour l'exemple illustratif, meilleurs que ceux obtenus avec un regulateur optimal. Vne structure generale de predicteur est proposee. Pour illustrer les resultats, des exemples de simulations sont montres
Approximation on Nash sets with monomial singularities
This paper is devoted to the approximation of differentiable semialgebraic
functions by Nash functions. Approximation by Nash functions is known for
semialgebraic functions defined on an affine Nash manifold M, and here we
extend it to functions defined on Nash subsets X of M whose singularities are
monomial. To that end we discuss first "finiteness" and "weak normality" for
such sets X. Namely, we prove that (i) X is the union of finitely many open
subsets, each Nash diffeomorphic to a finite union of coordinate linear
varieties of an affine space and (ii) every function on X which is Nash on
every irreducible component of X extends to a Nash function on M. Then we can
obtain approximation for semialgebraic functions and even for certain
semialgebraic maps on Nash sets with monomial singularities. As a nice
consequence we show that m-dimensional affine Nash manifolds with divisorial
corners which are class k semialgebraically diffeomorphic, for k>m^2, are also
Nash diffeomorphic.Comment: 39 page
A Prediction approach to introduce dead-time process control in a basic control course
7TH IFAC SYMPOSIUM ON ADVANCES IN CONTROL EDUCATION. 21/06/2006. MADRIDThis paper presents a methodology to introduce the control of dead-time processes using a simple and intuitive predictive approach. A trivial solutionfor the control of a process with a dead-time is first proposed. From this strategythe idea of the predictor based controller is derived. Open-loop predictors andclosed-loop ones are then used to analyze the obtained solution. A simple tuningof the proposed structure for a first order plus dead-time process together with apolynomial approximation of the dead-time allows to derive apidcontroller. Thus,the approach based on the idea of prediction can be used to interpret the use of apidto control a dead-time process. It is illustrated how the performance of thepidcontroller is limited by the modelling error introduced in the approximation. Thepresented approach gives a measurement of the achievable performance. Severalsimulation examples illustrate the results.Ministerio de Ciencia y Tecnología DPI 2005-0456
Consistency of Bayesian procedures for variable selection
It has long been known that for the comparison of pairwise nested models, a
decision based on the Bayes factor produces a consistent model selector (in the
frequentist sense). Here we go beyond the usual consistency for nested pairwise
models, and show that for a wide class of prior distributions, including
intrinsic priors, the corresponding Bayesian procedure for variable selection
in normal regression is consistent in the entire class of normal linear models.
We find that the asymptotics of the Bayes factors for intrinsic priors are
equivalent to those of the Schwarz (BIC) criterion. Also, recall that the
Jeffreys--Lindley paradox refers to the well-known fact that a point null
hypothesis on the normal mean parameter is always accepted when the variance of
the conjugate prior goes to infinity. This implies that some limiting forms of
proper prior distributions are not necessarily suitable for testing problems.
Intrinsic priors are limits of proper prior distributions, and for finite
sample sizes they have been proved to behave extremely well for variable
selection in regression; a consequence of our results is that for intrinsic
priors Lindley's paradox does not arise.Comment: Published in at http://dx.doi.org/10.1214/08-AOS606 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Robust PID tuning. Application to a Mobile Robot Pathtraking problem.
IFAC Digital Control: Past,Present and Future of PlO Control.Terrassa.Spain.2000This paper presents a methodology for tuning PIDs considering the nominal performance and the robustness as control specifications. The synthesis procedure is similar to the Ziegler-Nichols method for PID controllers and can be easily used for industrial processes. As a workbench for testing the PID controller a mobile robot has been used. The path tracking problem of a mobile robot has been used as a workbench for testing the PID controller
A Robust Adaptive Dead-Time Compensator with Application to A Solar Collector Field
This paper describes an easy-to-use PI controller with dead-time compensation that presents robust behaviour and can be applied to plants with variable dead-time. The formulation is based on an adaptive Smith predictor structure plus the addition of a filter acting on the error between the output and its prediction in order to improve robustness. The implementation of the control law is straightforward, and the filter needs no adjustment, since it is directly related to the plant dead-time. An application to an experimentally validated nonlinear model of a solar plant shows that this controller can improve the performance of classical PID controllers without the need of complex calculations.Ministerio de Ciencia y Tecnología TAP95-37
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