Predictive Linear Online Tracking for Unknown Targets

Anastasios Tsiamis, Aren Karapetyan, Yueshan Li, Efe C. Balta, John Lygeros
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:48657-48694, 2024.

Abstract

In this paper, we study the problem of online tracking in linear control systems, where the objective is to follow a moving target. Unlike classical tracking control, the target is unknown, non-stationary, and its state is revealed sequentially, thus, fitting the framework of online non-stochastic control. We consider the case of quadratic costs and propose a new algorithm, called predictive linear online tracking (PLOT). The algorithm uses recursive least squares with exponential forgetting to learn a time-varying dynamic model of the target. The learned model is used in the optimal policy under the framework of receding horizon control. We show the dynamic regret of PLOT scales with $\mathcal{O}(\sqrt{TV_T})$, where $V_T$ is the total variation of the target dynamics and $T$ is the time horizon. Unlike prior work, our theoretical results hold for non-stationary targets. We implement our online control algorithm on a real quadrotor, thus, showcasing one of the first successful applications of online control methods on real hardware.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-tsiamis24a, title = {Predictive Linear Online Tracking for Unknown Targets}, author = {Tsiamis, Anastasios and Karapetyan, Aren and Li, Yueshan and Balta, Efe C. and Lygeros, John}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {48657--48694}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/tsiamis24a/tsiamis24a.pdf}, url = {https://proceedings.mlr.press/v235/tsiamis24a.html}, abstract = {In this paper, we study the problem of online tracking in linear control systems, where the objective is to follow a moving target. Unlike classical tracking control, the target is unknown, non-stationary, and its state is revealed sequentially, thus, fitting the framework of online non-stochastic control. We consider the case of quadratic costs and propose a new algorithm, called predictive linear online tracking (PLOT). The algorithm uses recursive least squares with exponential forgetting to learn a time-varying dynamic model of the target. The learned model is used in the optimal policy under the framework of receding horizon control. We show the dynamic regret of PLOT scales with $\mathcal{O}(\sqrt{TV_T})$, where $V_T$ is the total variation of the target dynamics and $T$ is the time horizon. Unlike prior work, our theoretical results hold for non-stationary targets. We implement our online control algorithm on a real quadrotor, thus, showcasing one of the first successful applications of online control methods on real hardware.} }
Endnote
%0 Conference Paper %T Predictive Linear Online Tracking for Unknown Targets %A Anastasios Tsiamis %A Aren Karapetyan %A Yueshan Li %A Efe C. Balta %A John Lygeros %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-tsiamis24a %I PMLR %P 48657--48694 %U https://proceedings.mlr.press/v235/tsiamis24a.html %V 235 %X In this paper, we study the problem of online tracking in linear control systems, where the objective is to follow a moving target. Unlike classical tracking control, the target is unknown, non-stationary, and its state is revealed sequentially, thus, fitting the framework of online non-stochastic control. We consider the case of quadratic costs and propose a new algorithm, called predictive linear online tracking (PLOT). The algorithm uses recursive least squares with exponential forgetting to learn a time-varying dynamic model of the target. The learned model is used in the optimal policy under the framework of receding horizon control. We show the dynamic regret of PLOT scales with $\mathcal{O}(\sqrt{TV_T})$, where $V_T$ is the total variation of the target dynamics and $T$ is the time horizon. Unlike prior work, our theoretical results hold for non-stationary targets. We implement our online control algorithm on a real quadrotor, thus, showcasing one of the first successful applications of online control methods on real hardware.
APA
Tsiamis, A., Karapetyan, A., Li, Y., Balta, E.C. & Lygeros, J.. (2024). Predictive Linear Online Tracking for Unknown Targets. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:48657-48694 Available from https://proceedings.mlr.press/v235/tsiamis24a.html.

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