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

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 the 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 the 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 to build models with less complexity and better accuracy. The efficacy of the proposed technique is illustrated by using numerical examples.