Dual Stochastic MPC for Systems with Parametric and Structural Uncertainty

Elena Arcari, Lukas Hewing, Max Schlichting, Melanie Zeilinger
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:894-903, 2020.

Abstract

Designing controllers for systems affected by model uncertainty can prove to be a challenge, especially when seeking the optimal compromise between the conflicting goals of identification and control. This trade-off is explicitly taken into account in the dual control problem, for which the exact solution is provided by stochastic dynamic programming. Due to its computational intractability, we propose a sampling-based approximation for systems affected by both parametric and structural model uncertainty. The approach proposed in this paper separates the prediction horizon in a dual and an exploitation part. The dual part is formulated as a scenario tree that actively discriminates among a set of potential models while learning unknown parameters. In the exploitation part, achieved information is fixed for each scenario, and open-loop control sequences are computed for the remainder of the horizon. As a result, we solve one optimization problem over a collection of control sequences for the entire horizon, explicitly considering the knowledge gained in each scenario, leading to a dual model predictive control formulation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-arcari20a, title = {Dual Stochastic MPC for Systems with Parametric and Structural Uncertainty}, author = {Arcari, Elena and Hewing, Lukas and Schlichting, Max and Zeilinger, Melanie}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {894--903}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/arcari20a/arcari20a.pdf}, url = {https://proceedings.mlr.press/v120/arcari20a.html}, abstract = {Designing controllers for systems affected by model uncertainty can prove to be a challenge, especially when seeking the optimal compromise between the conflicting goals of identification and control. This trade-off is explicitly taken into account in the dual control problem, for which the exact solution is provided by stochastic dynamic programming. Due to its computational intractability, we propose a sampling-based approximation for systems affected by both parametric and structural model uncertainty. The approach proposed in this paper separates the prediction horizon in a dual and an exploitation part. The dual part is formulated as a scenario tree that actively discriminates among a set of potential models while learning unknown parameters. In the exploitation part, achieved information is fixed for each scenario, and open-loop control sequences are computed for the remainder of the horizon. As a result, we solve one optimization problem over a collection of control sequences for the entire horizon, explicitly considering the knowledge gained in each scenario, leading to a dual model predictive control formulation.} }
Endnote
%0 Conference Paper %T Dual Stochastic MPC for Systems with Parametric and Structural Uncertainty %A Elena Arcari %A Lukas Hewing %A Max Schlichting %A Melanie Zeilinger %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-arcari20a %I PMLR %P 894--903 %U https://proceedings.mlr.press/v120/arcari20a.html %V 120 %X Designing controllers for systems affected by model uncertainty can prove to be a challenge, especially when seeking the optimal compromise between the conflicting goals of identification and control. This trade-off is explicitly taken into account in the dual control problem, for which the exact solution is provided by stochastic dynamic programming. Due to its computational intractability, we propose a sampling-based approximation for systems affected by both parametric and structural model uncertainty. The approach proposed in this paper separates the prediction horizon in a dual and an exploitation part. The dual part is formulated as a scenario tree that actively discriminates among a set of potential models while learning unknown parameters. In the exploitation part, achieved information is fixed for each scenario, and open-loop control sequences are computed for the remainder of the horizon. As a result, we solve one optimization problem over a collection of control sequences for the entire horizon, explicitly considering the knowledge gained in each scenario, leading to a dual model predictive control formulation.
APA
Arcari, E., Hewing, L., Schlichting, M. & Zeilinger, M.. (2020). Dual Stochastic MPC for Systems with Parametric and Structural Uncertainty. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:894-903 Available from https://proceedings.mlr.press/v120/arcari20a.html.

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