Identification of Linear Parameter-Varying Systems Using B-splines

This paper brings B-splines into LPV system identification to express the model dependency on the scheduling parameter(s) and presents a strategy to control the complexity of this dependency. The higher the number of B-splines, the more complex the model. Since the number of B-splines building a spline is proportional to the number of knots partitioning the domain over which the spline is defined, the core of the strategies proposed in this paper is the selection of the optimal number and locations of the knots. A dedicated measure of significance of a knot combined with a unique grouping of the model state-space matrices and ℓ
₁
-norm regularization yielded two new methods: the Regularized State-space Model Interpolation of Local Estimates and the Regularized NLS-based LPV system identification approach.