Identification for generalized Hammerstein models with multiple switching linear dynamics

Abstract

Generalized Hammerstein models are defined as a type of Hammerstein models with a specific structure, consisting of a static nonlinear submodel connected with multiple switching dynamic linear submodels. They offer a separate structured representation for the overall static gains and changing dynamic characteristics of nonlinear systems, facilitating nonlinear inverse compensation and robust controller design for efficient control. This paper proposes a method for identifying generalized Hammerstein models and measuring their modeling uncertainties. Specifically, a generalized Hammerstein model activated by multiple validity functions is established, and its optimal parameter vector is estimated by solving a nonlinear and nonconvex optimization problem. Modeling uncertainties of generalized Hammerstein models are measured by some suboptimal parameter vectors according to fuzzy set theory. These vectors have the properties that their objective function values are close to the optimal one and their simulated outputs can reproduce certain measured outputs. In numerical and experimental examples, the proposed method establishes a generalized Hammerstein model that can well describe nonlinear systems with changing dynamic characteristics, and provides accurate and compact measurements of modeling uncertainties. By contrast, existing Hammerstein model identification methods yield inaccurate results due to model structural errors.