Subspace identification of Hammerstein models with interval uncertainties

Abstract

This work presents a novel method for identifying uncertain Hammerstein models in the state-space. The uncertainties of both the nonlinear static and linear dynamic blocks are represented by intervals. The limits of the model’s uncertain parameters are estimated by solving a nonlinear optimization problem, generated from the combination of subspace identification methods with interval arithmetic techniques. Unlike methodologies based on orthonormal functions, the proposed method does not require prior knowledge of the system dynamics. Additionally, the proposed methodology reduces the number of optimization problems and constraints needed to estimate the model parameters, compared to the technique that uses orthonormal functions. Simulated and experimental results illustrate the accuracy and precision of the estimates obtained by the proposed method.