Worst-case identification of Hammerstein models based on l∞ gain

We propose a new model set identification method for nonlinear systems described by the generalized Hammerstein model. While the existing method evaluates the parametric error based on the assumption that the true plant and the nominal model have the same structure, the proposed method evaluates the non-parametric error due to the unmodeled dynamics by l_∞ gain compatible with robust l₁ control, and gives a local model set near an equilibrium point for the given input level. Although it is generally quite difficult to evaluate the non-parametric error bound of the nonlinear systems based on finite experimental data, the upper bound of l_∞ gain can be obtained based on the impulse response estimates and their error bounds by taking account of a special property of l_∞ gain. Also, this method gives less conservative model sets with more experimental data by using the noise set which consists of hard-bounded noises, taking into account of a low correlation property of noise signals, simultaneously. Moreover, the effectiveness of this method is shown by a numerical example