Iterative Algorithm for Feedback Nonlinear Systems by Using the Maximum Likelihood Principle

This paper aims to find a maximum likelihood least squares-based iterative algorithm to solve the identification issues of closed-loop input nonlinear equation-error systems. By adopting the key term separation technique, the parameters of the forward channel are identified separately from the parameters of the feedback channel to address the cross-product terms. The hierarchical identification principle is introduced to decompose the original system into two subsystems for reduced computational complexity. The iterative estimation theory and the maximum likelihood principle are applied to design a new least-squares algorithm with high estimation accuracy by taking full use of all the measured input-output data at each iterative computation. Compared with the recursive least-squares (RELS) method. The simulation results verify theoretical findings, and the proposed algorithm can generate more accurate parameter estimates than the RELS algorithm.