Research on the stability of non‐equigap grey control model under multiple transformations

The purpose of this paper is to deal with the ill‐conditioned problem for the non‐equigap GM(1,1) control model by using the method of multiple transformations.

Owing to noises and interferences from both inside and outside of the system, many control systems contain unequal intervals and sharp variation which may result in undesirable systems instability. In order to ensure the stability and efficiency of grey forecasting control model, the data transformation for a raw series is an important and useful method for enhancing accuracy and improving ill‐condition of the non‐equigap GM(1,1) model.

This paper discusses the quantitative relations between the multiple transformation and the parameters of the non‐equigap GM(1,1) model in detail, and studies the effect of the multiple transformation on the condition number of the non‐equigap GM(1,1) model.

Accessibility and availability of data are the main limitations based on which model will be applied.

Choosing an appropriate multiple of transformation cannot only eliminate dimension, lessen computation and maintain high accuracy, but also largely reduce the condition number of the model and improve the ill‐condition of non‐equigap GM(1,1) model effectively.

This paper seems to be the first to discuss the stability problems for the non‐equigap GM(1,1) model.