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Publicações

Publicações por Paulo Santos

2004

Robust MOESP type algorithm with improved efficiency on the estimation of input matrices

Autores
Delgado, CJM; dos Santos, PL;

Publicação
SICE 2004 ANNUAL CONFERENCE, VOLS 1-3

Abstract
In this paper, a new approach to estimate matrices B and D, in subspace methods, is provided. The starting point was one method proposed by Van Overschee and De Moor (1996). We have derived new (and simpler) expressions and we found that the original method can be rewritten as a weighted least squares problem, involving the future outputs and inputs and the observability matrix.

2004

On subspace system identification algorithms implemented through sequences of modified householder algorithms

Autores
Delgado, CJM; dos Santos, PL;

Publicação
MSV'04 & AMCS'04, PROCEEDINGS

Abstract
In this paper we present two subspace identification methods implemented through sequences of modified Householder algorithm. The main idea was to show that subspace identification methods can be represented as sequences of least squares problems and implemented wing QR factorizations. Therefore, it is possible to develop iterative algorithms with most of the advantages of this kind of methods, and still improve the numerical efficiency, in order to deal with real-tme applications and minimize the computational burden.

2004

Recursive MOESP Type Subspace Identification Algorithm

Autores
Delgado, CJM; Santos, PLd;

Publicação
ICINCO 2004, Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, Setúbal, Portugal, August 25-28, 2004

Abstract

2004

Exploring the Linear Relations in the Estimation of Matrices B and D in Subspace Identification Methods

Autores
Delgado, CJM; Santos, PLd;

Publicação
ICINCO 2004, Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, Setúbal, Portugal, August 25-28, 2004

Abstract

2014

LPV system identification using a separable least squares support vector machines approach

Autores
dos Santos, PL; Azevedo Perdicoulis, TP; Ramos, JA; Deshpande, S; Rivera, DE; de Carvalho, JLM;

Publicação
2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC)

Abstract
In this article, an algorithm to identify LPV State Space models for both continuous-time and discrete-time systems is proposed. The LPV state space system is in the Companion Reachable Canonical Form. The output vector coefficients are linear combinations of a set of a possibly infinite number of nonlinear basis functions dependent on the scheduling signal, the state matrix is either time invariant or a linear combination of a finite number of basis functions of the scheduling signal and the input vector is time invariant. This model structure, although simple, can describe accurately the behaviour of many nonlinear SISO systems by an adequate choice of the scheduling signal. It also partially solves the problems of structural bias caused by inaccurate selection of the basis functions and high variance of the estimates due to over-parameterisation. The use of an infinite number of basis functions in the output vector increases the flexibility to describe complex functions and makes it possible to learn the underlying dependencies of these coefficients from the data. A Least Squares Support Vector Machine (LS-SVM) approach is used to address the infinite dimension of the output coefficients. Since there is a linear dependence of the output on the output vector coefficients and, on the other hand, the LS-SVM solution is a nonlinear function of the state and input matrix coefficients, the LPV system is identified by minimising a quadratic function of the output function in a reduced parameter space; the minimisation of the error is performed by a separable approach where the parameters of the fixed matrices are calculated using a gradient method. The derivatives required by this algorithm are the output of either an LTI or an LPV (in the case of a time-varying SS matrix) system, that need to be simulated at every iteration. The effectiveness of the algorithm is assessed on several simulated examples.

2017

LPV system identification using the matchable observable linear identification approach

Autores
dos Santos, PL; Romano, R; Azevedo Perdicoulis, TP; Rivera, DE; Ramos, JA;

Publicação
2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC)

Abstract
This article presents an optimal estimator for discrete-time systems disturbed by output white noise, where the proposed algorithm identifies the parameters of a Multiple Input Single Output LPV State Space model. This is an LPV version of a class of algorithms proposed elsewhere for identifying LTI systems. These algorithms use the matchable observable linear identification parameterization that leads to an LTI predictor in a linear regression form, where the ouput prediction is a linear function of the unknown parameters. With a proper choice of the predictor parameters, the optimal prediction error estimator can be approximated. In a previous work, an LPV version of this method, that also used an LTI predictor, was proposed; this LTI predictor was in a linear regression form enablin, in this way, the model estimation to be handled by a Least-Squares Support Vector Machine approach, where the kernel functions had to be filtered by an LTI 2D-system with the predictor dynamics. As a result, it can never approximate an optimal LPV predictor which is essential for an optimal prediction error LPV estimator. In this work, both the unknown parameters and the state-matrix of the output predictor are described as a linear combination of a finite number of basis functions of the scheduling signal; the LPV predictor is derived and it is shown to be also in the regression form, allowing the unknown parameters to be estimated by a simple linear least squares method. Due to the LPV nature of the predictor, a proper choice of its parameters can lead to the formulation of an optimal prediction error LPV estimator. Simulated examples are used to assess the effectiveness of the algorithm. In future work, optimal prediction error estimators will be derived for more general disturbances and the LPV predictor will be used in the Least-Squares Support Vector Machine approach.

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