Multi-step ahead predictions for multi variable linear stochastic systems via model recursion

Abstract

The multi-step ahead prediction method for the output of a multi-variable linear discrete-time stochastic system, directly based on the recursion of system model, is developed. The basic procedures are: (1) rewrite the original system model into a one-step ahead recursive version; (2) repeatedly use this recursion step by step and thus successively gain all the required multi-step ahead predictions. It is proved that this model recursion method is strictly equivalent to the existing method using the recursion of multi-variable Diophantine equation, under the condition of white noise. The proposed method possesses advantages both in computational reduction and programming simplicity, and has successfully been used in a multi-variable modified generalized predictive controller.