Computational load reduction in bounded error identification of Hammerstein systems

In this technical note we present a procedure for the identification of Hammerstein systems from measurements affected by bounded noise. First, we show that computation of tight parameter bounds requires the solution to nonconvex optimization problems where the number of decision variables increases with the length of the experimental data sequence. Then, in order to reduce the computational burden of the identification problem, we propose a procedure to relax the formulated problem into a collection of polynomial optimization problems where the number of variables does not depend on the number of measurements. Advantages of the presented approach with respect to previously published results are discussed and highlighted by means of a simulation example.