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arXiv · 2404.08955

Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop

Rodrigo A. González·Siqi Pan·Cristian R. Rojas·James S. Welsh
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Abstract

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.

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Rodrigo A. González, Siqi Pan, Cristian R. Rojas, James S. Welsh. 2024-04-13. Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop. https://arxiv.org/abs/2404.08955

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