Linear system identification using the sequential stabilizing spline algorithm

Abstract

Paradoxically, even if stability (with its many facets) is the key concept in control, including system stability constraints in an identification procedure is still an unresolved puzzle under many aspects. In fact, also in the linear setting there is no procedure proposed in the literature able to estimate the dominant pole of a dynamic system ensuring stability. In this paper, we design a new algorithm, namely the sequential stabilizing spline (SSS) algorithm, which fills this gap. Our approach determines the system’s stability radius by combining Gaussian regression and stochastic simulation, using stable spline kernels to model the one-step ahead predictor impulse responses. Then, a stable model is recovered through a novel sequential convex optimization procedure whose computational time is orders of magnitude faster than approaches based on linear matrix inequalities (LMI). Numerical experiments are included and show that SSS can return models with high long-term predictive capability. SSS performance is comparable to that achieved by classical prediction error methods equipped with an oracle that has access to the test set to tune the best model order for any prediction horizon.