Conditions for parameter unidentifiability of linear ARX systems for enhancing security

Xiangyu Mao, Jianping He, Chengpu Yu, Chongrong Fang
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:890-901, 2024.

Abstract

For an adversarial observer of parametric systems, the identifiability of parameters reflects the possibility of inferring the system dynamics and then affects the performance of attacks against the systems. Hence, achieving unidentifiability of the parameters, which makes the adversary unable to get identification with low variance, is an attractive way to enhance security. In this paper, we propose a quantitative definition to measure the unidentifiability based on the lower bound of identification variance. The lower bound is given via the analysis of the Fisher Information Matrix (FIM). Then, we propose the necessary and sufficient condition for unidentifiability and derive the explicit form of the unidentifiability condition for linear autoregressive systems with exogenous inputs (ARX systems). It is proved that the unidentifiability of linear ARX systems can be achieved through quadratic constraints on inputs and outputs. Finally, considering an optimal control problem with security concerns, we apply the unidentifiability constraint and obtain the optimal controller. Simulations demonstrate the effectiveness of our method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-mao24b, title = {Conditions for parameter unidentifiability of linear {ARX} systems for enhancing security}, author = {Mao, Xiangyu and He, Jianping and Yu, Chengpu and Fang, Chongrong}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {890--901}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/mao24b/mao24b.pdf}, url = {https://proceedings.mlr.press/v242/mao24b.html}, abstract = {For an adversarial observer of parametric systems, the identifiability of parameters reflects the possibility of inferring the system dynamics and then affects the performance of attacks against the systems. Hence, achieving unidentifiability of the parameters, which makes the adversary unable to get identification with low variance, is an attractive way to enhance security. In this paper, we propose a quantitative definition to measure the unidentifiability based on the lower bound of identification variance. The lower bound is given via the analysis of the Fisher Information Matrix (FIM). Then, we propose the necessary and sufficient condition for unidentifiability and derive the explicit form of the unidentifiability condition for linear autoregressive systems with exogenous inputs (ARX systems). It is proved that the unidentifiability of linear ARX systems can be achieved through quadratic constraints on inputs and outputs. Finally, considering an optimal control problem with security concerns, we apply the unidentifiability constraint and obtain the optimal controller. Simulations demonstrate the effectiveness of our method.} }
Endnote
%0 Conference Paper %T Conditions for parameter unidentifiability of linear ARX systems for enhancing security %A Xiangyu Mao %A Jianping He %A Chengpu Yu %A Chongrong Fang %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-mao24b %I PMLR %P 890--901 %U https://proceedings.mlr.press/v242/mao24b.html %V 242 %X For an adversarial observer of parametric systems, the identifiability of parameters reflects the possibility of inferring the system dynamics and then affects the performance of attacks against the systems. Hence, achieving unidentifiability of the parameters, which makes the adversary unable to get identification with low variance, is an attractive way to enhance security. In this paper, we propose a quantitative definition to measure the unidentifiability based on the lower bound of identification variance. The lower bound is given via the analysis of the Fisher Information Matrix (FIM). Then, we propose the necessary and sufficient condition for unidentifiability and derive the explicit form of the unidentifiability condition for linear autoregressive systems with exogenous inputs (ARX systems). It is proved that the unidentifiability of linear ARX systems can be achieved through quadratic constraints on inputs and outputs. Finally, considering an optimal control problem with security concerns, we apply the unidentifiability constraint and obtain the optimal controller. Simulations demonstrate the effectiveness of our method.
APA
Mao, X., He, J., Yu, C. & Fang, C.. (2024). Conditions for parameter unidentifiability of linear ARX systems for enhancing security. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:890-901 Available from https://proceedings.mlr.press/v242/mao24b.html.

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