System Identification of Multivariate Systems With Feedback

Abstract

System identification of linear stochastic systems has been the concern of many scientists and engineers. The same system can be described in many ways and consequently many different models have been proposed. However, the complexity of the systems and computational difficulty, especially under the presence of feedback and external disturbances, have rendered identification a difficult task. This paper deals with a general modeling procedure that can be used for identification of feedback systems. First, a brief discussion on the joint input-output process models is given, followed by the discussion on the canonical representation of the model. A simplified model is derived from the general vector model. This will lead to the validity of using the Modified Autoregressive Moving Average Vector (MARMAV) model in the identification of the general multivariate system with open-loop and closed-loop dynamics. Next, an estimation procedure is explained. The estimation is pursued to reach a maximum likelihood model by nonlinear iterative calculations. Since initial values are required to start the procedure which are critical to the estimation, two methods for the initial guess value estimation are provided in the appendices.