Kernel-based identification of asymptotically stable continuous-time linear dynamical systems

ABSTRACT

In many engineering applications, continuous-time models are preferred to discrete-time ones, in that they provide good physical insight and can be derived also from non-uniformly sampled data. However, for such models, model selection is a hard task if no prior physical knowledge is given. In this paper, we propose a non-parametric approach to infer a continuous-time linear model from data, by automatically selecting a proper structure of the transfer function and guaranteeing to preserve the system stability properties. By means of benchmark simulation examples, the proposed approach is shown to outperform state-of-the-art continuous-time methods, also in the critical case when short sequences of canonical input signals, like impulses or steps, are used for model learning.

Keywords:

• Kernel-based learning
• linear identification
• continuous-time identification

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Here, the notion of ‘low excitation’ is not referring to the spectral density of the theoretical impulse and step signals, which have a flat spectrum, but to the spectrum of their finite time realizations, which are known not to share the same excitation properties.

2 In the case of experiments with impulsive input, one solution to perform system identification is to leverage output data by using subspace methods.