Identification of stable linear systems via the sequential stabilizing spline algorithm

Abstract

Stability of identified models can be achieved, in the framework of parametric Prediction Error Methods (PEM) by imposing nonlinear constraints on the parameter space. When using regularisation techniques with, for instance, stable spline kernels, stability of the predictor model is guaranteed; however this does not imply stability of the model, nor there is a trivial way to guarantee the identified model is stable. An important approach available in the literature to recover stability relies on linear matrix inequalities (LMI). In particular, by means of overparametrization, a convex optimization problem is formulated. Its solution has to balance adherence to a preliminarily obtained (unconstrained) estimate and system stability according to a design parameter δ that determines dominant poles location. In this paper we propose a new stabilization algorithm. Our approach is non convex but does not require overparametrization and embeds regularization through the use of Gaussian regression and stable spline kernels. It is implemented by a very efficient sequential convex optimization procedure, namely the sequential stabilizing spline (SSS) algorithm. In comparison with LMI, numerical experiments show that SSS can provide more predictive models with a computational time orders of magnitude faster.