A multi-step approach for modeling MIMO systems from input-output data

This paper proposes a multi-step approach for building discrete time models of MIMO systems from input-output data. The black box approach to system modeling is assumed. The given MIMO system is decomposed into a number of MISO systems. The mean square error is chosen as the quality index. From the data the algorithm builds a linear model, a polynomial approximation model and a fuzzy model in sequence. The algorithm automatically terminates as and when a model of desired accuracy is obtained. If the nonlinear system is separable, then the algorithm reduces the model complexity further by building a hybrid model as an aggregation of simpler linear and nonlinear models. To distinguish linear and nonlinear components, fuzzy models are built using the linear form of Sugeno inference for relaxed systems and linear affine form of Sugeno inference for non relaxed systems. The interpretability coefficients are obtained in one matrix by rearranging the terms. The properties of the system, which are not known a priori can be deduced from the interpretability matrix. Thus the multi-step technique helps build models with lesser complexity and better accuracy The efficacy of the proposed technique is illustrated using numerical examples.