Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop
<|reference_start|>Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop: Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results.<|reference_end|>
@article{gonzález2024consistency,
    title={Consistency analysis of refined instrumental variable methods for
  continuous-time system identification in closed-loop},
    author={Rodrigo A. Gonz'alez, Siqi Pan, Cristian R. Rojas, James S. Welsh},
    journal={arXiv preprint arXiv:2404.08955},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.08955},
    primaryClass={eess.SY cs.SY}
}