Identification Methods

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Mobile Robots: Tracking Control
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New Approaches to H-Infinity Control II
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Lyapunov's 2nd Method
Robotics: Tracking Control
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Applied Nonlinear Control

Author Index
A B C D E F G H I
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Set Membership Identification of Nonlinear Systems

Authors:

Carlo Novara, Mario Milanese,

Volume: 1, Page 2831 Paper number 2099

Abstract:

In this paper we investigate the problem of finding upper and lower bounds of a real valued function of several variables, on the base of a set of noise corrupted values of the function evaluated at a given set of variables and on some assumptions on function regularity and on noise bounds. Several set membership linear and nonlinear identification problems can be recast into the above problem. Two solutions are proposed. The first one is quite straightforward and leads to the definition of bounds that are the tightest ones but, in high dimensional spaces, computationally expensive. The second solution, relying on approximation properties of neural networks, leads to the evaluation of somewhat more conservative bounds, whose computational complexity is significantly lower than for the optimal bounds. A numerical example, related to the identification and prediction of a Lorenz chaotic system, is presented to show the effectiveness of the proposed approach.

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Criterion For Selection Of Model And Controller Design Based On I/O Data

Authors:

Kouji Tsumura, Hidenori Kimura,

Volume: 1, Page 2837 Paper number 2009

Abstract:

In this paper, we propose information criteria not only for model estimation and selection but also for selection of design method of controller. The criteria are derived by the same approach of AIC/TIC, however we consider the modeling of the distribution of the control performance substituting for that of system index. The criteria are composed of a log-likelihood function and a bias term similar to AIC/TIC, and especially the bias term depends on the controller. Moreover, when the controller is designed under some conditions, the criteria become stochastic variables and their expectations are further added by the other bias terms, which are in proportion to the dimension of the control parameter. This shows that model estimation, selection and control designing are influenced simultaneously by the complexity of model and that of controller.

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Identification Of Systems With Direction-Dependent Dynamics

Authors:

H.A. Barker, Keith R. Godfrey, Ai Hui Tan,

Volume: 1, Page 2843 Paper number 1265

Abstract:

In this paper, the identification of systems with direction-dependent dynamics by means of bilinear models and Wiener models is considered. It is shown that when such systems are perturbed by pseudo-random binary signals based on maximum-length sequences, distinctive patterns are observed in the cross-correlation between the system input and system output. These patterns are not present when other kinds of pseudo-random binary signals are used. The patterns obtained for bilinear models and Wiener models are similar, and both depend on the characteristic polynomial of the maximum-length sequence used. For the case in which the dynamics involved are first-order, analytical results are obtained which allow the patterns to be compared in detail. The results expected when the pseudo-random signals used are inverse-repeat are also described. It is concluded that both kinds of model are suitable for use in this application, provided that the model parameters are appropriately chosen.

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Identification of Multivariable Hammerstein Systems Using Rational Orthonormal Bases

Authors:

Juan C. Gómez, Enrique Baeyens,

Volume: 1, Page 2849 Paper number 1755

Abstract:

In this paper, a non iterative algorithm for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein systems is presented. The proposed algorithm is numerically robust, since it is based only on least squares estimation and singular value decomposition. Under weak assumptions on the persistency of excitation of the inputs, the algorithm provides consistent estimates even in the presence of coloured noise. Key in the derivation of the results is the use of rational orthonormal bases for the representation of the linear part of the system. An additional advantage of this is the possibility of incorporating prior information about the system in a typically black-box identification scheme.

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Asymptotic Properties of Hammerstein Model Estimates

Authors:

Dietmar Bauer, Brett Ninness,

Volume: 1, Page 2855 Paper number 1750

Abstract:

This paper considers the estimation of Hammerstein models. The main result of the paper lies in a specification of a set of sufficient conditions on the input sequence, the noise (and the true system) in order to ensure that a non-linear least-squares approach enjoys properties of consistency and asymptotic normality and furthermore, that an estimate of the parameter covariance matrix is also consistent. The set of assumptions is specified using the concept of near epoch dependence, which has been developed in the econometrics literature. Indeed, one purpose of this paper is to highlight the usefulness of this concept in the context of analysing estimation procedures for nonlinear dynamical systems. This setup is utilized in an example, where the static nonlinearity is due to input saturation.

CD001750.PDF (From Author)

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Recurrent Neural Networks For Identification Of Nonlinear Systems

Authors:

Xuemei Ren, Shumin Fei,

Volume: 1, Page 2861 Paper number 109

Abstract:

A new type of recurrent neural network is discussed in this paper, which provides the potential for the modelling of unknown nonlinear systems with multi-inputs and multi-outputs. The proposed network is a generalization of the network described by Elman. It is shown that the proposed network with appropriate neurons in the context layer can model unknown nonlinear systems. Based on the PID-like training objective function, the learning algorithm of the proposed network is considerably faster through the introduction of dynamic backpropagation, which is used to estimate the weights of both the feedforward and feedback connections. The techniques have been successfully applied to the modelling nonlinear plants and simulation results are included.

CD000109.PDF (From Author) CD000109.PDF (Scanned)

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Frequency Domain Curve Fitting: A Global Approach

Authors:

Olav Slupphaug,

Volume: 1, Page 2867 Paper number 1157

Abstract:

We consider the problem of fitting fixed order rational SISO transfer functions to frequency response data using a least squares criterion. The main contribution is showing how this problem can be solved semi-globally by transforming it into a bilinear matrix inequality (BMI) problem. The BMI problem is in turn solved by a branch-and-bound approach. An application is given to 'linearization' of a complex dynamic multi-phase flow simulator.

CD001157.PDF (From Author)

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