Improved Gravitational Search and Gradient Iterative Identification for Multivariable Hammerstein Time-Delay Systems

Multivariable Hammerstein time-delay (MHTD) systems have been widely used in a variety of complex industrial systems; thus, it is of great significance to identify the parameters of such systems. The MHTD system is difficult to identify due to its inherent complexity. As one of heuristic algorithms, the gravitational search algorithm is suitable for identifying such complex models, but it has the problem of easily falling into local optimum. Therefore, this paper combines the improved chaotic gravitational search algorithm (ICGSA) and gradient iterative (GI) algorithm and proposes an ICGSA-GI algorithm to overcome the shortcomings of the above two algorithms. Then, we use it to identify the unknown parameters of the MHTD systems. Finally, a numerical example and an application case are given for validating the feasibility of the three identification methods. The results demonstrate that the three algorithms can identify the unknown parameters of the MHTD system effectively. In addition, by comparing with ICGSA and GI algorithms, this paper confirms that the ICGSA-GI algorithm behaves better than ICGSA and GI algorithm in identification accuracy, and the convergence speed of the ICGSA-GI algorithm is faster than that of the GI algorithm.

Automated summary

This paper proposes an improved chaotic gravitational search algorithm (ICGSA) combined with the gradient iterative (GI) algorithm, called the ICGSA-GI algorithm, to identify the parameters of multivariable Hammerstein time-delay (MHTD) systems. The feasibility of the algorithm is demonstrated through numerical and application examples, showing that the ICGSA-GI algorithm can effectively identify the unknown parameters of the MHTD system and outperforms the ICGSA and GI algorithms in terms of identification accuracy and convergence speed.