Identification Of Continuous-time Nonlinear Systems Research Articles

Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation

ABSTRACTIn this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation.

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

Although a vast number of techniques for the identification of nonlinear discrete-time systems have been introduced, the identification of continuous-time nonlinear systems is still extremely difficult. In this paper, the Nonlinear Difference Equation with Moving Average noise (NDEMA) model which is a general representation of nonlinear systems and contains, as special cases, both continuous-time and discrete-time models, is first proposed. Then based on this new representation, a systematic framework for the identification of nonlinear continuous-time models is developed. The new approach can not only detect the model structure and estimate the model parameters, but also work for noisy nonlinear systems. Both simulation and experimental examples are provided to illustrate how the new approach can be applied in practice.

Identification of Continuous-time Nonlinear Systems via Local Gaussian Process Models

This paper deals with a nonparametric identification of continuous-time nonlinear systems using multiple local Gaussian process (GP) models. Multiple sets of training input and output data are collected to train the local GP prior models. Each local GP prior model is trained by minimizing the negative log marginal likelihood of each set of the training data. The final nonlinear function with confidence measure is estimated by weighted mean of the local estimated nonlinear functions using the predictive variances of local GP posterior distributions. Compared to the standard GP-based identification method, the proposed method can reduce the computational cost and improve the accuracy of identification. Simulation results are shown to illustrate the effectiveness of the proposed identification method.

SYSTEM IDENTIFICATION USING FRACTIONAL HAMMERSTEIN MODELS

Identification of continuous-time non-linear systems characterised by fractional order dynamics is studied. The Riemann-Liouville definition of fractional differentiation is used. A new identification method is proposed through the extension of Hammerstein-type models by allowing their linear part to belong to the class of fractional models. Fractional models are compact and so are used here to model complex dynamics with few parameters.

Continuous time non-linear system identification in the frequency domain

A new algorithm, for identifying non-linear differential equation models, is introduced. The algorithm avoids the computation of derivatives by using the generalized frequency response functions to reconstruct the model. It is shown that the model can be constructed sequentially by building in first the linear terms, then the quadratic terms and so on and provides unbiased estimates in the presence of noise. A simulated example and the identification of a model relating the action of waveforces on an offshore structure are included to demonstrate the procedure.

A modified neural network for dynamical system identification and control

ABSTRAC This paper presents a new type of neural network in which the dynamical error feedback is used to modify the inputs of the network. A new identification model constructed by the proposed network and stable filters is used for continuous time nonlinear system identification, which can achieve the superior modeling performance over the standard feedforward networks. In addition, stable adaptive control scheme based on the proposed networks is developed. Several simulation results are provided to demonstrate the effectiveness of the proposed methods

Wavelet neural networks for continuous time nonlinear system identification

Abstract In this paper, a wavelet-based neural network (WNN) is introduced for continuous nonlinear system identification. The adaptive weight learning laws are derived based on Lyapunov stability theory for static and dynamical system identification respectively. It is proved that the identification error will converge to zero and the weight will be bounded in the case of no modeling error. Simulation results demonstrate the effectiveness of the proposed identification methodology.

Identification of continuous-time nonlinear systems via local linear equations united by automatic choosing function and genetic algorithm

This paper deals with an identification method of continuous-time nonlinear systems using a model expanded by a basis of automatic choosing functions (ACF). Higher order derivatives of input and output data are estimated by a delayed state variable filter, or the Butterworth filter. An unknown nonlinear function to be estimated is approximately described by local linear equations united by ACF. The resulting model is linear in the parameters, which are estimated by the least-squares method. The model structure and Butterworth filter are properly determined by a genetic algorithm. Simulation results are shown to demonstrate the effectiveness of the proposed method.

自動抽出関数展開モデルと遺伝的アルゴリズムを用いた連続時間非線形システムの同定

自動抽出関数展開モデルと遺伝的アルゴリズムを用いた連続時間非線形システムの同定

A recurrent network for dynamic system identification

This paper presents a type of recurrent artificial neural network architecture for identification of an arbitrary, continuous dynamic system. The recurrent network is shown to be stable for a constant input with certain conditions on the parameters of the network. The proposed network has significant advantages over similar models in continuous time nonlinear system identification and is used to identify three nonlinear dynamic systems. Finally, the applicability of the radial basis function networks using the same network architecture to reduce the time-complexity of the training task is presented.