Convex approximations for a bi-level formulation of data-enabled predictive control

Xu Shang, Yang Zheng
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:1071-1082, 2024.

Abstract

The Willems’ fundamental lemma, which characterizes linear time invariant (LTI) systems using input and output trajectories, has found many successful applications. Combining this with receding horizon control leads to a popular Data-EnablEd Predictive Control (DeePC) scheme. DeePC is first established for LTI systems and has been extended and applied for practical systems beyond LTI settings. However, the relationship between different DeePC variants, involving regularization and dimension reduction, remains unclear. In this paper, we first discuss a bi-level optimization formulation that combines a data pre-processing step as an inner problem (system identification) and predictive control as an outer problem (online control). We next introduce a series of convex approximations by relaxing some hard constraints in the bi-level optimization as suitable regularization terms, accounting for an implicit identification. These include some existing DeePC variants as well as two new variants, for which we establish their equivalence under appropriate settings. Notably, our analysis reveals a novel variant, called DeePC-SVD-Iter, which has remarkable empirical performance of direct methods on systems beyond deterministic LTI settings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-shang24a, title = {Convex approximations for a bi-level formulation of data-enabled predictive control}, author = {Shang, Xu and Zheng, Yang}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {1071--1082}, 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/shang24a/shang24a.pdf}, url = {https://proceedings.mlr.press/v242/shang24a.html}, abstract = {The Willems’ fundamental lemma, which characterizes linear time invariant (LTI) systems using input and output trajectories, has found many successful applications. Combining this with receding horizon control leads to a popular Data-EnablEd Predictive Control (DeePC) scheme. DeePC is first established for LTI systems and has been extended and applied for practical systems beyond LTI settings. However, the relationship between different DeePC variants, involving regularization and dimension reduction, remains unclear. In this paper, we first discuss a bi-level optimization formulation that combines a data pre-processing step as an inner problem (system identification) and predictive control as an outer problem (online control). We next introduce a series of convex approximations by relaxing some hard constraints in the bi-level optimization as suitable regularization terms, accounting for an implicit identification. These include some existing DeePC variants as well as two new variants, for which we establish their equivalence under appropriate settings. Notably, our analysis reveals a novel variant, called DeePC-SVD-Iter, which has remarkable empirical performance of direct methods on systems beyond deterministic LTI settings.} }
Endnote
%0 Conference Paper %T Convex approximations for a bi-level formulation of data-enabled predictive control %A Xu Shang %A Yang Zheng %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-shang24a %I PMLR %P 1071--1082 %U https://proceedings.mlr.press/v242/shang24a.html %V 242 %X The Willems’ fundamental lemma, which characterizes linear time invariant (LTI) systems using input and output trajectories, has found many successful applications. Combining this with receding horizon control leads to a popular Data-EnablEd Predictive Control (DeePC) scheme. DeePC is first established for LTI systems and has been extended and applied for practical systems beyond LTI settings. However, the relationship between different DeePC variants, involving regularization and dimension reduction, remains unclear. In this paper, we first discuss a bi-level optimization formulation that combines a data pre-processing step as an inner problem (system identification) and predictive control as an outer problem (online control). We next introduce a series of convex approximations by relaxing some hard constraints in the bi-level optimization as suitable regularization terms, accounting for an implicit identification. These include some existing DeePC variants as well as two new variants, for which we establish their equivalence under appropriate settings. Notably, our analysis reveals a novel variant, called DeePC-SVD-Iter, which has remarkable empirical performance of direct methods on systems beyond deterministic LTI settings.
APA
Shang, X. & Zheng, Y.. (2024). Convex approximations for a bi-level formulation of data-enabled predictive control. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:1071-1082 Available from https://proceedings.mlr.press/v242/shang24a.html.

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