Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Abstract

Summary This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.

Parameter estimation of multiple‐input single‐output Hammerstein controlled autoregressive system based on improved adaptive moment estimation algorithm

“…Ding et al presented the multi‐innovation stochastic gradient algorithm and the multi‐innovation least squares algorithm for linear stochastic systems 28,29 . Fan and Lin used the swarm intelligence method to search the parameter identification of MISO‐H model and transformed the parameter identification problem into the optimal solution problem of nonlinear function, then proposed an improved particle swarm optimization; 30 Ahmadi et al proposed an identification algorithm based on a mixture of inverse de Casteljau algorithm, least squares method, and the Levenberg‐Marquart algorithm; 31 Naitali used the continuous excitation of deterministic signals for parameter identification of MISO‐H systems; 32 Rahmani et al proposed the identification of MISO neuro‐fractional‐order Hammerstein system based on the Lyapunov stability theory 33 …”

“…28,29 Fan and Lin used the swarm intelligence method to search the parameter identification of MISO-H model and transformed the parameter identification problem into the optimal solution problem of nonlinear function, then proposed an improved particle swarm optimization; 30 Ahmadi et al proposed an identification algorithm based on a mixture of inverse de Casteljau algorithm, least squares method, and the Levenberg-Marquart algorithm; 31 Naitali used the continuous excitation of deterministic signals for parameter identification of MISO-H systems; 32 Rahmani et al proposed the identification of MISO neuro-fractional-order Hammerstein system based on the Lyapunov stability theory. 33 Several types of identification algorithms have been proposed, such as the least squares method, 34,35 the gradient methods, [36][37][38] the hierarchical methods, [39][40][41] and so on. The adaptive moment estimation (ADAM) method is an important optimization method with good statistical properties.…”

Auxiliary model‐based multi‐innovation recursive identification algorithms for an input nonlinear controlled autoregressive moving average system with variable‐gain nonlinearity

“…Mathematical models are the basis of analyzing and designing control systems 1‐4 . For decades, many state and parameter estimation algorithms have been carried out for linear systems, 5 bilinear systems, 6 and nonlinear systems 7 . Nonlinear models are widespread in industrial production and social activities.…”

Modified particle filtering‐based robust estimation for a networked control system corrupted by impulsive noise

“…In such a scenario, the performance of the identification algorithm under Gaussian noise, such as the least squares algorithm, may significantly degrade since its quadratic criterion function amplifies the prediction errors so that the outliers are likely to dominate all the observations 30,31 . To weaken the impact of the non‐Gaussian noise to the parameter estimation, Rahmani and Farrokhi proposed a Lyapunov method for the fractional‐order system with outliers, which were modeled by the product sequences of a Bernoulli distribution and a uniform distribution 32 . Yang et al presented an expectation maximization algorithm for a nonlinear system with missing data, in which the outliers were modeled by the Student's t ‐distribution 33 .…”