Identification of linear parameter-varying systems: A reweighted ℓ2,1-norm regularization approach

This paper presents a regularized nonlinear least-squares identification approach for linear parameter-varying (LPV) systems. The objective of the method is, on the one hand, to obtain an LPV model of which the response fits the system measurements as accurately as possible and, on the other hand, to favor models with an as simple as possible dependency on the scheduling parameter. This is accomplished by introducing ℓ2,1-norm regularization into the nonlinear least-squares problem. The resulting nonsmooth optimization problem is reformulated into a nonlinear second-order cone program and solved using a sequential convex programming approach. Through an iterative reweighting of the regularization, the parameters that do not substantially contribute to the system response are penalized heavily, while the significant parameters remain unaffected or are penalized only slightly. Numerical and experimental validations of the proposed method show a substantial model simplification in comparison with the nonregularized solution, without significantly sacrificing model accuracy.