Abstract
Hammerstein systems are formed by a static nonlinear block followed by a dynamic linear block. To solve the parameterizing difficulty caused by parameter coupling between the nonlinear part and the linear part in a Hammerstein system, an instrumental variable method is studied to parameterize the Hammerstein system. To achieve in simultaneously identifying parameters and orders of the Hammerstein system and to promote the computational efficiency of the identification algorithm, a sparsity-seeking orthogonal matching pursuit (OMP) optimization method of compressive sensing is extended to identify parameters and orders of the Hammerstein system. The idea is, by the filtering technique and the instrumental variable method, to transform the Hammerstein system into a simple form with a separated nonlinear expression and to parameterize the system into an autoregressive model, then to perform an instrumental variable-based orthogonal matching pursuit (IV-OMP) identification method for the Hammerstein system. Simulation results illustrate that the investigated method is effective and has advantages of simplicity and efficiency.
Highlights
Nonlinear system modeling and identification are very important in theory and application [1,2,3,4,5,6]; block-oriented nonlinear systems, which combine nonlinear and linear blocks in various styles, are the typical representation of nonlinear systems
(iv) Simulation results illustrate that the investigated method is effective and has advantages of simplicity and efficiency
To solve the parameterizing difficulty caused by parameter coupling between the nonlinear part and the linear part in a Hammerstein system, firstly, by filtering the equation of the linear block with the coefficient function of the controlled term, we separate the parameter coupling between the linear block and the nonlinear block
Summary
Nonlinear system modeling and identification are very important in theory and application [1,2,3,4,5,6]; block-oriented nonlinear systems, which combine nonlinear and linear blocks in various styles, are the typical representation of nonlinear systems. To achieve in simultaneously identifying parameters and orders and to promote the computational efficiency of the estimated method, a sparsity-seeking orthogonal matching pursuit optimization method of compressive sensing is extended to identify parameters and orders of the Hammerstein systems. Complexity autoregressive form, and to perform the instrumental variable-based orthogonal matching pursuit (IV-OMP) identification method for the Hammerstein systems. An instrumental variable-based orthogonal matching pursuit (IV-OMP) algorithm is investigated to simultaneously estimate the orders and parameters of a Hammerstein system. (ii) To achieve in simultaneously identifying parameters and orders and to promote the computational efficiency of the system, an instrumental variablebased orthogonal matching pursuit (IV-OMP) optimization method of compressive sensing is extended to identify parameters and orders of the systems.
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