Continuous-time Hammerstein Systems Research Articles

Frequency Domain Identification of Continuous-Time Hammerstein Systems With Adaptive Continuous-Time Rational Orthonormal Basis Functions

In this paper, we propose a new identification method for continuous-time Hammerstein systems. This method is based on the adaptive generalized rational orthonormal basis functions. In particular, we use the strategy in which poles of basis functions are selected one by one in terms of a criterion. By doing this, we not only take advantage of the variability of the generalized orthogonal basis functions, but also reduce the computational burden. The proposed algorithm is adaptive. Meanwhile, convergence analysis is performed with considering the sampling frequency, noise level, sampling length, and terms of basis functions. The obtained results guarantee the convergence of the whole Hammerstein system. Finally, a numerical example is presented to illustrate the usefulness of the proposed identification algorithm.

A hybrid metaheuristic algorithm for identification of continuous-time Hammerstein systems

This paper presents a new hybrid identification algorithm called the Average Multi-Verse Optimizer and Sine Cosine Algorithm for identifying the continuous-time Hammerstein system. In this paper, two modifications were employed on the conventional Multi-Verse Optimizer. Our first modification was an average design parameter updating mechanism to solve the local optima issue. The second modification was the hybridization of Multi-Verse Optimizer with Sine Cosine Algorithm that will balance the exploration and exploitation processes and thus improve the poor searching capability. The proposed hybrid method was used for identifying the parameters of linear and nonlinear subsystems in the Hammerstein model using the given input and output data. A continuous-time linear subsystem was considered in this study, while there were a few methods that utilize such models. Furthermore, various nonlinear subsystems such as the quadratic and hyperbolic functions had been used in those experiments. The efficiency of the novel technique is illustrated using a numerical example and two real-world applications, which are a twin rotor system and a flexible manipulator system. The numerical and experimental results analysis were observed with respect to the convergence curve of the fitness function, the parameter deviation index, time-domain and frequency-domain responses of the identified model, and the Wilcoxon's rank test. The results showed that the proposed method was efficient in identifying both the Hammerstein model subsystems in terms of the quadratic output estimation error and parameter deviation index. The proposed hybrid method also achieved better performance in modeling of the twin-rotor system as well as the flexible manipulator system and provided better solutions compared to other optimization methods including Particle Swarm Optimizer, Grey Wolf Optimizer, Multi-Verse Optimizer and Sine Cosine Algorithm.

Recursive identification of multiple-input single-output fractional-order Hammerstein model with time delay

This paper deals with identification of the continuous-time Hammerstein systems with time delay using Genetic Algorithm (GA) combined with the Recursive Least-Squares (RLS) method. This model consists of the Radial Basis Function Neural Network (RBFNN) as its nonlinear static part and fractional order transfer function as its dynamic linear part. The fractional orders are identified by GA with an innovative strategy called Modified Genetic Algorithm (MGA). The main innovative idea is the selection and transferring the best characteristics or properties to the next generation. On the other hand, the centers and widths and the weighting parameters of the RBFNN and the transfer function coefficients of the linear dynamic part are updated by the RLS method. Simulation results are applied to illustrate the proposed method accuracy.

Identification of continuous-time Hammerstein systems by simultaneous perturbation stochastic approximation

This paper proposes an identification method for Hammerstein systems using simultaneous perturbation stochastic approximation (SPSA). Here, the structure of nonlinear subsystem is assumed to be unknown, while the structure of linear subsystem, such as the system order, is assumed to be available. The main advantage of the SPSA-based method is that it can be applied to identification of Hammerstein systems with less restrictive assumptions. In order to clarify this point, piecewise affine functions with a large number of parameters are adopted to approximate the unknown nonlinear subsystems. Furthermore, the linear subsystems are supposed to be described in continuous-time. Though this class of systems closely reflects the actual systems, there are few methods to identify such models. Hence, the SPSA-based method is utilized to identify the parameters in both linear and nonlinear subsystems simultaneously. The effectiveness of the proposed method is evaluated through several numerical examples. The results demonstrate that the proposed algorithm is useful to obtain accurate models, even for high-dimensional parameter identification.

Erratum to: Non-parametric identification of continuous-time Hammerstein systems using Gaussian process model and particle swarm optimization

This paper deals with a non-parametric identification of continuous-time Hammerstein systems using Gaussian process (GP) models. A Hammerstein system consists of a memoryless non-linear static part followed by a linear dynamic part. The identification model is derived using the GP prior model which is described by the mean function vector and the covariance matrix. This prior model is trained by the separable least-squares (LS) approach combining the linear LS method with particle swarm optimization to minimize the negative log marginal likelihood of the identification data. Then the non-linear static part is estimated by the predictive mean function of the GP, and the confidence measure of the estimated non-linear static part is evaluated by the predictive covariance function of the GP. Simulation results are shown to illustrate the proposed method.

Non-parametric identification of continuous-time Hammerstein systems using Gaussian process model and particle swarm optimization

Non-parametric identification of continuous-time Hammerstein systems using Gaussian process model and particle swarm optimization

Iterative Identification of Continuous-Time Hammerstein and Wiener Systems Using a Two-Stage Estimation Algorithm

This article presents an iterative method to deal with the identification of continuous-time single-input/single-output Hammerstein and Wiener systems, characterized by a series connection of a nonlinear static element and a linear dynamic element. The internal variable between the nonlinear and linear elements is inaccessible to measurements so that simultaneous parameter estimation of the two elements cannot be easily achieved in a least-squares fashion. This difficulty could be circumvented by updating the internal variable at each iteration step. A two-stage estimation algorithm, in conjunction with moving-horizon smoothing and a solution-guiding mechanism, is established to ensure the convergence and accuracy of the iterative method in the face of linear structure mismatch, high static nonlinearity with an unknown characteristic, and severe noise. At the first stage, a good description of the static nonlinearity is given by a multisegment function or a polynomial in an iterative manner. Linear structure mismatch is allowed for this stage of estimation. At the second stage, the identification problem is reduced to a simple linear one with the internal variable gained at the first stage. A noniterative procedure can then be applied to determine accurately the structure and parameters of the linear dynamic element. Studies with simulated and experimental examples demonstrate that the proposed identification method is valid for a wide variety of nonlinear system dynamics and test conditions.

On-line Identification of Continuous-time Hammerstein Systems via RBF Networks and Immune Algorithm

On-line Identification of Continuous-time Hammerstein Systems via RBF Networks and Immune Algorithm

Continuous-Time Hammerstein System Identification From Sampled Data

A continuous-time Hammerstein system driven by a random signal is identified from observations sampled in time. The sampling may be uniform or not. The a-priori information about the system is nonparametric, functional forms of both the nonlinear characteristic and the impulse response are completely unknown. Three kernel algorithms, one offline and two semirecursive are presented. Their convergence to the true characteristic of the nonlinear subsystem is shown. The distance between consecutive sampling times must not decrease too fast for the algorithms to converge.

Recursive identification of continuous-time Hammerstein systems

A continuous-time Hammerstein system is identified. The characteristic of its nonlinear subsystem and the impulse response of the dynamic parts are estimated from observations taken at input and output of the whole system. All algorithms are of the on-line type. Their convergence is shown. Results of simulation examples are also presented.

Continuous-time Hammerstein system identification

A continuous-time Hammerstein system, i.e., a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one, is identified. The system is driven and disturbed by white random signals. The a priori information about both subsystems is nonparametric, which means that functional forms of both the nonlinear characteristic and the impulse response of the dynamic subsystem are unknown. An algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown. The impulse response of the dynamic part is recovered with a correlation method. The algorithms are computationally independent. Results of a simulation example are given.