Abstract
Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the structure of the lifted models using the traditional lifting technique. Furthermore, an auxiliary model-based multi-innovation stochastic gradient algorithm is presented to estimate the parameters involved in the linear and nonlinear blocks. The simulation results confirm that the proposed algorithm is effective and can achieve a high estimation performance.
Highlights
The dynamics of most practical systems are inherently nonlinear due to complex physical, chemical and biological mechanisms
The Hammerstein model represents a class of input nonlinear systems, where the nonlinear block is prior to the linear one
On the basis of that work, this paper aims to propose a δ−1 -based model to describe periodically non-uniformly sampled-data Hammerstein systems and presents an auxiliary model-based multi-innovation stochastic gradient (SG)
Summary
The dynamics of most practical systems are inherently nonlinear due to complex physical, chemical and biological mechanisms. For periodically non-uniformly sampled-data Hammerstein systems, Li et al derived the lifted transfer function model by means of the lifting technique and presented a least squares-based iterative algorithm for parameter estimation [32]. To simplify the model structure and reduce the identification complexity, Xie et al put forward a novel input-output representation of linear systems with non-uniform sampling by introducing a time-varying backward shift operator δ−1 [35]. On the basis of that work, this paper aims to propose a δ−1 -based model to describe periodically non-uniformly sampled-data Hammerstein systems and presents an auxiliary model-based multi-innovation SG algorithm to estimate the model parameters.
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