Optimal structure identification of bilinear-Laguerre model from input/output observations

This paper proposes a new approach to identify an optimal structure with respect to the truncating orders of the new nonlinear bilinear-Laguerre model. This latter is used to describe a nonlinear system with a parametric complexity reduction resulting from the expansion of the bilinear model on independent and orthonormal Laguerre bases. The proposed structural identification approach is investigated to guarantee from input/output observations a more accurate model approximation of the system with significant parameter reduction. This is achieved by identifying the optimal truncating orders characterizing the model's structure. This approach is based only on the filtered input/output of the system by defining a specific matrix, which becomes singular when the truncating orders are close to their optimal values. According to the matrix singularity of the specific matrix by varying the truncating orders, we propose a structural identification algorithm where an estimation indicator is considered to achieve the optimal structure identification. This technique allows us to calculate the optimal truncating orders where the noise influence is studied. It is tested in numerical examples based on the bilinear-Laguerre model with a variable structure by changing the value of the truncating orders. As well, experimental validation is retained on a 2-degree-of-freedom (DoF) helicopter system. Simulation and experimental results show the effectiveness of the proposed optimal structure identification approach.