Parameter estimation of multiple-input single-output Hammerstein controlled autoregressive system based on improved adaptive moment estimation algorithm

In this article, the problem of parameter estimation for a multiple-input single-output Hammerstein controlled autoregressive (MISO-HCAR) model is solved. After establishing the identification model of MISO-HCAR system, an improved adaptive moment estimation algorithm with decreasing weight (IADAM) is proposed. The improved algorithm transforms the nonlinear system identification problem into a parameter space optimization problem, according to the input and output data obtained from the system, and uses the parallel search ability of the IADAM algorithm to estimate all the parameters of the system simultaneously. Two numerical examples and the case study example of chemical continuously stirred tank reactor (CSTR) system show that the proposed IADAM algorithm with decreasing weight has better identification effect on the MISO-HCAR model and CSTR system than the stochastic gradient descent (SGD) algorithm and the basic adaptive moment estimation (ADAM) algorithm, and the estimation accuracy and convergence speed are greatly improved. Thus, the IADAM can estimate the parameters of the MISO-HCAR system and the CSTR system more effectively.