Identification of Hammerstein Systems with Set-Valued Observations

This work is concerned with identification of Hammerstein systems whose outputs are measured by set-valued sensors. The system consists of a memoryless nonlinearity which is polynomial and possibly non-invertible, followed by a linear subsystem. The parameters of linear and nonlinear parts are unknown but have known orders. Input design, identification algorithms, and their essential properties are presented under the assumptions that the distribution function of the noise is known and the threshold values of set-valued sensors are known. The concept of strongly scaled full rank signals is introduced to capture the essential conditions under which the Hammerstein system can be identified with set-valued observations. Under strongly scaled full rank conditions, a strongly convergent algorithm is constructed. The unbias and efficient properties of the algorithm are investigated.