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.
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.
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.
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.
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.
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.
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.
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