Multivariate polynomial decoupling in nonlinear system identification

To understand, predict and control the dynamical systems in the world surrounding us, mathematical models are created and analyzed. Such a model can be linear or nonlinear, depending on the application at hand. In order to better approximate the nonlinear effects of real world systems, recent years have shown a growing shift of the research attention from linear modeling to nonlinear modeling. Even though nonlinear models can be quite accurate, they also tend to become very complex and difficult to understand. Trying to use a model consisting of thousand of different parameters will decrease intuitive and physical comprehension and industrial acceptance. That is why these complex models should be approximated by simpler methods, while keeping the understanding and predictive power of the non-linear behavior. During this research project, we have focused our attention to two special, though widely used, sorts of nonlinear models, called block-oriented models and nonlinear state-space models. These models contain a complex multiple-input multiple-output static nonlinearity, which we have studied and structured in a simpler way. For this, multidemensional mathematical tools, called tensor decompositions, offered a good starting point for the so-called decoupling process.