655 research outputs found
Grammar-based Representation and Identification of Dynamical Systems
In this paper we propose a novel approach to identify dynamical systems. The
method estimates the model structure and the parameters of the model
simultaneously, automating the critical decisions involved in identification
such as model structure and complexity selection. In order to solve the
combined model structure and model parameter estimation problem, a new
representation of dynamical systems is proposed. The proposed representation is
based on Tree Adjoining Grammar, a formalism that was developed from linguistic
considerations. Using the proposed representation, the identification problem
can be interpreted as a multi-objective optimization problem and we propose a
Evolutionary Algorithm-based approach to solve the problem. A benchmark example
is used to demonstrate the proposed approach. The results were found to be
comparable to that obtained by state-of-the-art non-linear system
identification methods, without making use of knowledge of the system
description.Comment: Submitted to European Control Conference (ECC) 201
Structure Selection of Polynomial NARX Models using Two Dimensional (2D) Particle Swarms
The present study applies a novel two-dimensional learning framework
(2D-UPSO) based on particle swarms for structure selection of polynomial
nonlinear auto-regressive with exogenous inputs (NARX) models. This learning
approach explicitly incorporates the information about the cardinality (i.e.,
the number of terms) into the structure selection process. Initially, the
effectiveness of the proposed approach was compared against the classical
genetic algorithm (GA) based approach and it was demonstrated that the 2D-UPSO
is superior. Further, since the performance of any meta-heuristic search
algorithm is critically dependent on the choice of the fitness function, the
efficacy of the proposed approach was investigated using two distinct
information theoretic criteria such as Akaike and Bayesian information
criterion. The robustness of this approach against various levels of
measurement noise is also studied. Simulation results on various nonlinear
systems demonstrate that the proposed algorithm could accurately determine the
structure of the polynomial NARX model even under the influence of measurement
noise
NARX-based nonlinear system identification using orthogonal least squares basis hunting
An orthogonal least squares technique for basis hunting (OLS-BH) is proposed to construct sparse radial basis function (RBF) models for NARX-type nonlinear systems. Unlike most of the existing RBF or kernel modelling methods, whichplaces the RBF or kernel centers at the training input data points and use a fixed common variance for all the regressors, the proposed OLS-BH technique tunes the RBF center and diagonal covariance matrix of individual regressor by minimizing the training mean square error. An efficient optimization method isadopted for this basis hunting to select regressors in an orthogonal forward selection procedure. Experimental results obtained using this OLS-BH technique demonstrate that it offers a state-of-the-art method for constructing parsimonious RBF models with excellent generalization performance
Hybrid algorithm for NARX network parameters' determination using differential evolution and genetic algorithm
A hybrid optimization algorithm using Differential Evolution (DE) and Genetic Algorithm (GA) is proposed in this study to address the problem of network parameters determination associated with the Nonlinear Autoregressive with eXogenous inputs Network (NARX-network). The proposed algorithm involves a two level optimization scheme to search for both optimal network architecture and weights. The DE at the upper level is formulated as combinatorial optimization to search for the network architecture while the associated network weights that minimize the prediction error is provided by the GA at the lower level. The performance of the algorithm is evaluated on identification of a laboratory rotary motion system. The system identification results show the effectiveness of the proposed algorithm for nonparametric model development
Hybrid algorithm for NARX network parameters' determination using differential evolution and genetic algorithm
A hybrid optimization algorithm using Differential Evolution (DE) and Genetic Algorithm (GA) is proposed in this study to address the problem of network parameters determination associated with the Nonlinear Autoregressive with eXogenous inputs Network (NARX-network). The proposed algorithm involves a two level optimization scheme to search for both optimal network architecture and weights. The DE at the upper level is formulated as combinatorial optimization to search for the network architecture while the associated network weights that minimize the prediction error is provided by the GA at the lower level. The performance of the algorithm is evaluated on identification of a laboratory rotary motion system. The system identification results show the effectiveness of the proposed algorithm for nonparametric model development
On the smoothness of nonlinear system identification
We shed new light on the \textit{smoothness} of optimization problems arising
in prediction error parameter estimation of linear and nonlinear systems. We
show that for regions of the parameter space where the model is not
contractive, the Lipschitz constant and -smoothness of the objective
function might blow up exponentially with the simulation length, making it hard
to numerically find minima within those regions or, even, to escape from them.
In addition to providing theoretical understanding of this problem, this paper
also proposes the use of multiple shooting as a viable solution. The proposed
method minimizes the error between a prediction model and the observed values.
Rather than running the prediction model over the entire dataset, multiple
shooting splits the data into smaller subsets and runs the prediction model
over each subset, making the simulation length a design parameter and making it
possible to solve problems that would be infeasible using a standard approach.
The equivalence to the original problem is obtained by including constraints in
the optimization. The new method is illustrated by estimating the parameters of
nonlinear systems with chaotic or unstable behavior, as well as neural
networks. We also present a comparative analysis of the proposed method with
multi-step-ahead prediction error minimization
Black-box modeling of nonlinear system using evolutionary neural NARX model
Nonlinear systems with uncertainty and disturbance are very difficult to model using mathematic approach. Therefore, a black-box modeling approach without any prior knowledge is necessary. There are some modeling approaches have been used to develop a black box model such as fuzzy logic, neural network, and evolution algorithms. In this paper, an evolutionary neural network by combining a neural network and a modified differential evolution algorithm is applied to model a nonlinear system. The feasibility and effectiveness of the proposed modeling are tested on a piezoelectric actuator SISO system and an experimental quadruple tank MIMO system
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