System Identification using the Multivariate Simplotope B-Spline

Abstract

In recent research efforts the multivariate simplex spline has shown great promise in system identification applications. It has high approximation power, while its linearity in the parameters allows for computationally efficient estimation of the coefficients. In this paper the multivariate simplotope spline is derived from this spline, and compared to its simplex counterpart in a system identification setting. Contrary to the simplex spline, the simplotope spline allows the user to incorporate expert knowledge of the system in his models. Whereas in the first spline all variables are included in a complete polynomial, in the latter the user can split the variables in decoupled subsets. By fitting models to specifically designed test functions it is shown that this can indeed improve the approximation performance in terms of both the error metrics and the number of B-coefficients required. This comes at the price of a higher total degree, and therefore an increased sensitivity to Runge's phenomenon in case of poor data distribution. Finally an attempt is made to apply the proposed methods to a set of flight data of the DelFly II, a flapping wing micro aerial vehicle. It is found that the used data set is not suitable for global system identification, as the data in concentrated in low-dimensional clusters in the five-dimensional state space. Therefore it is advised that a more suitable data set is obtained to validate the simplotope spline in a system identification setting.