Stochastic Gradient Algorithm for Hammerstein Systems with Piece-Wise Linearities - Intelligent Computing for Sustainable Energy and Environment - page 241

Stochastic Gradient Algorithm for Hammerstein
Systems with Piece-Wise Linearities
Jing Chen 1 , 2 and Jia Chen 1
1 Wuxi Professional College of Science and Technology, Wuxi, P.R. China 214028
[e-mail]
2 Control Science and Engineering Research Center, Jiangnan University,
Wuxi, P.R. China 214122
[e-mail]
Abstract. This paper studies a stochastic algorithm for Hammerstein
systems with piece-wise linearities. By using a switching function, the
model of the nonlinear Hammerstein systems be changed to an identi-
fication model, then based on the derived model, a stochastic gradient
identification algorithm is used to estimate all the unknown parameters
of the systems. An example is provided to show the effectiveness of the
proposed algorithm.
Keywords: Piece-wise linearity, Stochastic gradient, Parameter estima-
tion, Hammerstein system.
1 Introduction
Hammerstein systems consist of a static nonlinear block followed by a linear
dynamic block which are widely used in many areas, e.g., nonlinear filtering,
actuator saturations, audio-visual processing, signal analysis. There exists a lot
of work on identification of these nonlinear systems [1-6]. Some work assumed
that the nonlinearity is the polynomial nonlinearity [6-8], others assumed that
the nonlinearity is the hard nonlinearity [2,3,9-12,14]. Hard nonlinearity can-
not be written as an analytic function of the input and is more common in
engineering practice. Recently, identification of Hammerstein systems with hard
nonlinearity has been received much attention [3,9,10,13-15]. For example, Bai
used a deterministic approach and the correlation analysis method to estimate
the parameters of systems with hard input nonlinearities [9]. Chen proposed
a novel estimation algorithm for dual-rate Hammerstein systems with preload
nonlinearity [13], and studied identification problems for Hammerstein systems
with saturation and dead-zone nonlinearities [3].
This paper deals with the identification of Hammerstein systems with piece-
wise linearities. By using the switching function, the model of the Hammerstein
systems can be turned into an identification model, then based on the derived
This work was supported by the National Natural Science Foundation of China.