Online Identification Of Nonlinear Systems Research Articles

Echo state networks for online, multi-step MPC relevant identification

This paper presents an online nonlinear system identification algorithm for model predictive control relevant identification, based on an echo state network (ESN) trained using the recursive least squares method with a directional forgetting factor. The proposed online ESN architecture is formed by a reservoir, with fixed recurrent connections, and a reservoir readout mechanism, which is updated online to define the network output. The ESN is used to perform a multi-step prediction task, which can be used for model-predictive control purposes. The proposed online identification algorithm is evaluated in simulation using a conical tank level process and compared with the results of other approaches from the literature. The results show that the proposed algorithm is able to identify the nonlinear characteristics of the process without considering any prior information about it. In addition, the results for long-range predictions are better than the ones obtained with a model linear in its parameters and several baseline ESN models from literature, after the adaptation phase of the proposed algorithm.

Networked model predictive control using a wavelet neural network

This study proposes using a wavelet neural network (WNN) with a feedforward component and a model predictive controller (MPC) for online nonlinear system identification and control over a communication network. The WNN performs the online identification of the nonlinear system. The MPC uses the model to predict the future outputs of the system over an extended prediction horizon and calculates the optimal future inputs by minimizing a controller cost function. A computationally efficient formulation for the controller is presented to reduce the computational complexity of the MPC for online implementation and Lyapunov theory is used to prove the stability of the MPC. The methodology is applied to the online identification and control of an unmanned autonomous vehicle. Simulation results show that the MPC with an extended prediction horizon can effectively control the system in the presence of fixed or random network delay.

Frequency domain spline adaptive filters

Spline adaptive filter (SAF) is a kind of simple and effective nonlinear system online identification method. When the length of FIR filter, which represents the linear sub-model, is very long, the computational complexity will increase dramatically. In order to solve this problem, a frequency domain spline adaptive filter (FDSAF) is proposed in this paper. The filtering and adaptive processes in FIR filter are implemented in frequency domain, which transforms convolution in time domain into multiplication in frequency domain. In FDSAF, the fast Fourier transform (FFT) and its inverse transform (IFFT) are utilized, and the overlap-save method is adopted in order to improve the computational efficiency. In this paper, detailed procedures of FDSAF are derived. In addition, the bound on learning rate and computational complexity of the algorithm are analyzed. Finally, several numerical experiments are implemented in order to verify the effectiveness of FDSAF, and the results show that the proposed FDSAF can significantly reduce the computational complexity on the premise of ensuring the convergence performance compared with the traditional time domain SAF algorithm.

Online identification of nonlinear systems using neo-fuzzy supported brain emotional learning network

Online identification of nonlinear systems using neo-fuzzy supported brain emotional learning network

A changing forgetting factor RLS for online identification of nonlinear systems based on ELM–Hammerstein model

In this paper, an online identification method is proposed for nonlinear system identification based on extreme learning machine (ELM)–Hammerstein model. The ELM–Hammerstein model comprises an ELM neural network followed by a linear dynamic subsystem. This model is linear in parameters and nonlinear in the input. To speed up the convergence and meanwhile improve identification accuracy, a changing forgetting factor recursive least squares (CFF-RLS) method is proposed as online learning algorithm. The algorithm can identify the parameters of linear dynamic subsystem and the weights of ELM neural network simultaneously. Simulation results verify the effectiveness of the proposed method.

온라인 GA 기반 비선형 시스템 식별

Genetic algorithm is known to be an effective method to solve a global nonlinear optimization. However, a huge amount of calculation is needed to improve the dependability of the solution and thus Ga is not adequate for online implementation. In this paper, we propose an online nonlinear system identification scheme which employs population feedback genetic algorithm. The effectiveness of our scheme is shown by several simulations.

Extended fuzzy function model with stable learning methods for online system identification

AbstractThe aim of the online nonlinear system identification is the accurate modeling of the current local input‐output behavior of the plant without using any prior knowledge and offline modeling phase. It is a challenging task for many intelligent systems when used for real‐time control applications. In this paper, we propose a novel computationally efficient extended fuzzy functions (EFF) model for system identification of unknown nonlinear discrete‐time systems. The main contributions are to introduce an effective quasi‐nonlinear model (EFF) and propose adaptive learning rates (ALR) for recursive least squares (RLS) and gradient‐descent (GD) methods. The asymptotic convergence of the modeling errors and boundedness of the parameters are proved by using the input‐to‐state stability (ISS) approach. Numerical simulations are performed for Box–Jenkins gas furnace system and a nonlinear dynamic system. The benefits of its accuracy, stability and simple implementation in practice indicate that EFF model is a promising technique for online identification of nonlinear systems. Copyright © 2010 John Wiley & Sons, Ltd.

Online identification of nonlinear system using reduced kernel principal component analysis

The Principal Component Analysis (PCA) is a powerful technique for extracting structure from possibly high-dimensional data sets. It is readily performed by solving an eigenvalue problem, or by using iterative algorithms that estimate principal components. This paper proposes a new method for online identification of a nonlinear system modelled on Reproducing Kernel Hilbert Space (RKHS). Therefore, the PCA technique is tuned twice, first we exploit the Kernel PCA (KPCA) which is a nonlinear extension of the PCA to RKHS as it transforms the input data by a nonlinear mapping into a high-dimensional feature space to which the PCA is performed. Second, we use the Reduced Kernel Principal Component Analysis (RKPCA) to update the principal components that represent the observations selected by the KPCA method.

Selective recursive kernel learning for online identification of nonlinear systems with NARX form

Online identification of nonlinear systems is still an important while difficult task in practice. A general and simple online identification method, namely Selective Recursive Kernel Learning (SRKL), is proposed for multi-input–multi-output (MIMO) systems with the nonlinear autoregressive with exogenous input form. A two-stage RKL online identification framework is first formulated, where the information contained by a sample (i.e., the new arriving or old useless one) can be introduced into and/or deleted from the model, recursively. Then, a sparsification strategy to restrict the model complexity is developed to guarantee all the output channels of the MIMO model accurate simultaneously. Specially, a novel pruning approach based on the fast leave-one-out cross-validation criterion is explored to acquire generalization ability by determining and then deleting the useless information. Consequently, the model can adaptively adjust its structure to capture the process dynamics. The SRKL method is applied intensively to several nonlinear systems for multifold identification aims. The obtained results show that SRKL is superior to traditional methods, e.g., artificial neural networks and fuzzy systems, in different situations. The benefits of its accuracy, reliable performance and simple implementation in practice indicate that SRKL is promising for online identification of nonlinear systems.

Nonlinear system identification using optimized dynamic neural network

In this paper, both off-line architecture optimization and on-line adaptation have been developed for a dynamic neural network (DNN) in nonlinear system identification. In the off-line architecture optimization, a new effective encoding scheme—Direct Matrix Mapping Encoding (DMME) method is proposed to represent the structure of neural network by establishing connection matrices. A series of GA operations are applied to the connection matrices to find the optimal number of neurons on each hidden layer and interconnection between two neighboring layers of DNN. The hybrid training is adopted to evolve the architecture, and to tune the weights and input delays of DNN by combining GA with the modified adaptation laws. The modified adaptation laws are subsequently used to tune the input time delays, weights and linear parameters in the optimized DNN-based model in on-line nonlinear system identification. The effectiveness of the architecture optimization and adaptation is extensively tested by means of two nonlinear system identification examples.

Parametric identification of robotic systems with stable time-varying Hopfield networks

In this work, a novel method for on-line identification of non-linear systems is proposed based upon the optimisation methodology with Hopfield neural networks. The original Hopfield model is adapted so that the weights of the resulting network are time-varying. A rigorous analytical study proves that, under mild assumptions, the estimations provided by the method converge to the actual parameter values in the case of constant parameters, or to a bounded neighbourhood of the parameters when these are time-varying. Time-varying parameters, often appearing in mechanical systems, are dealt with by the neural estimator in a more natural way than by least squares techniques. Both sudden and slow continuous variations are considered. Besides, in contrast to the gradient method, the neural estimator does not critically depend on the adjustment of the gain. The proposed method is applied to the identification of a robotic system with a flexible link. A reduced output prediction error and an accurate estimation of parameters are observed in simulation results.

Passivity analysis for dynamic multilayer neuro identifier

In this work, dynamic multilayer neural networks are used for nonlinear system online identification. The passivity approach is applied to access several stability properties of the neuro identifier. The conditions for passivity, stability, asymptotic stability, and input-to-state stability are established. We conclude that the commonly-used backpropagation algorithm with a modification term which is determined by offline learning may make the neuro identification algorithm robustly stable with respect to any bounded uncertainty.

Some new results on system identification with dynamic neural networks

Nonlinear system online identification via dynamic neural networks is studied in this paper. The main contribution of the paper is that the passivity approach is applied to access several new stable properties of neuro identification. The conditions for passivity, stability, asymptotic stability, and input-to-state stability are established in certain senses. We conclude that the gradient descent algorithm for weight adjustment is stable in an L(infinity) sense and robust to any bounded uncertainties.

Multilayer dynamic neural networks for non-linear system on-line identification

To identify on-line a quite general class of non-linear systems, this paper proposes a new stable learning law of the multilayer dynamic neural networks. A Lyapunov-like analysis is used to derive this stable learning procedure for the hidden layer as well as for the output layer. An algebraic Riccati equation is considered to construct a bound for the identification error. The suggested learning algorithm is similar to the well-known backpropagation rule of the multilayer perceptrons but with an additional term which assure the stability property of the identification error.

On-line identification of nonlinear systems using Volterra polynomial basis function neural networks

An on-line identification scheme using Volterra polynomial basis function (VPBF) neural networks is considered for nonlinear control systems. This comprises a structure selection procedure and a recursive weight learning algorithm. The orthogonal least-squares algorithm is introduced for off-line structure selection and the growing network technique is used for on-line structure selection. An on-line recursive weight learning algorithm is developed to adjust the weights so that the identified model can adapt to variations of the characteristics and operating points in nonlinear systems. The convergence of both the weights and the estimation errors is established using a Lyapunov technique. The identification procedure is illustrated using simulated examples.

A new system identification technique using Kaiman filtering and multilayer neural networks

The objective of this work is to use the back-propagation algorithm in conjunction with Kaiman filtering in order to establish a new self-learning technique of multilayer neural network (MNN). This new technique is developed by directly building a Kaiman filtering model for each perceptron in order to increase the adaptability of the MNN and to provide for on-line nonlinear system identification. We demonstrate that this new technique is faster and more stable than the classical back-propagation algorithm for training multilayer perceptrons. We also find that it is less sensitive to the initial weights and to the learning parameters.