Recursive identification of multi-variable interconnected systems

Abstract

In the field of identification of multi-input multi-output (MIMO) systems, the methods may be divided into two principal groups, according to the model structure: the state-space formulation and the input-output description in terms of transfer functions. A MIMO system, described by the last representation can be decomposed into ny interconnected subsystems, where ny is the number of outputs. These subsystems can be decomposed into single-input single-output subsystems which are the transfer functions of the model. The transfer function output is called ‘partial output’ the transfer function input may be either a general input of the system or a partial output of another transfer function or a white noise. This representation has two principal advantages in identification: a minimal number of parameters must be identified and parameters have direct system meaning. A disadvantage is the unmeasurable partial output, which must be estimated. A procedure is suggested that uses estimates of the partial output in a recursive way. This method identifies the input-output and noise-dynamics of the multi-variable system contaminated by coloured noise, using a simple stage estimator. Extension to some non-linear cases is suggested.