Convergence of normalized iterative identification of Hammerstein systems

An iterative identification algorithm of Hammerstein systems needs a proper initial condition to guarantee its convergence. In this paper, we propose a new algorithm by fixing the norm of the parameter estimates. The normalized algorithm ensures the convergence property under arbitrary nonzero initial conditions. The proofs of the property also give a geometrical explanation on why the normalization guarantees the convergence. An additional contribution is that the static function in the Hammerstein system is extended to square-integrable functions.

► We propose a new algorithm by fixing the norm of the parameter estimates.
► The normalized algorithm ensures the convergence property under arbitrary nonzero initial conditions.
► We give a geometrical explanation on why the normalization guarantees the convergence.
► The static function in the Hammerstein system is extended to square-integrable functions.