Recursive identification for Hammerstein–Wiener systems with dead-zone input nonlinearity

• A new method is proposed for the recursive identification of the Hammerstein–Wiener systems.
• The input block of this system contains dead-zone nonlinearity.
• The behavior of parameter convergence is analyzed and the conditions of uniform convergence are obtained.
• An adaptive form of a weighted factor is adopted to enhance the algorithm convergence.
• The application of this algorithm can be easily expanded to the Hammerstein systems.

A new recursive algorithm is proposed for the identification of a special form of Hammerstein–Wiener system with dead-zone nonlinearity input block. The direct motivation of this work is to implement on-line control strategies on this kind of system to produce adaptive control algorithms. With the parameterization model of the Hammerstein–Wiener system, a special form of model estimation error is defined; and then its approximate formula is given for the following derivation. Based on these, a recursive identification algorithm is established that aims at minimizing the sum of the squared parameter estimation errors. The conditions of uniform convergence are obtained from the property analysis of the proposed algorithm and an adaptive setting method for a weighted factor in the algorithm is given, which enhances the convergence of the proposed algorithm. This algorithm can also be used for the identification of the Hammerstein systems with dead-zone nonlinearity input block. Three simulation examples show the validity of this algorithm.