Exploiting Model Sparsity in Adaptive MPC: A Compressed Sensing Viewpoint

Monimoy Bujarbaruah, Charlott Vallon
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:137-146, 2020.

Abstract

This paper proposes an Adaptive Stochastic Model Predictive Control (MPC) strategy for stable linear time-invariant systems in the presence of bounded disturbances. We consider multi-input, multi-output systems that can be expressed by a Finite Impulse Response (FIR) model. The parameters of the FIR model corresponding to each output are unknown but assumed sparse. We estimate these parameters using the Recursive Least Squares algorithm. The estimates are then improved using set-based bounds obtained by solving the Basis Pursuit Denoising problem. Our approach is able to handle hard input constraints and probabilistic output constraints. Using tools from distributionally robust optimization, we reformulate the probabilistic output constraints as tractable convex second-order cone constraints, which enables us to pose our MPC design task as a convex optimization problem. The efficacy of the developed algorithm is highlighted with a thorough numerical example, where we demonstrate performance gain over the counterpart algorithm of Bujarbaruah et al. (2018), which does not utilize the sparsity information of the system impulse response parameters during control design.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-bujarbaruah20a, title = {Exploiting Model Sparsity in Adaptive MPC: A Compressed Sensing Viewpoint}, author = {Bujarbaruah, Monimoy and Vallon, Charlott}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {137--146}, 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/bujarbaruah20a/bujarbaruah20a.pdf}, url = {https://proceedings.mlr.press/v120/bujarbaruah20a.html}, abstract = {This paper proposes an Adaptive Stochastic Model Predictive Control (MPC) strategy for stable linear time-invariant systems in the presence of bounded disturbances. We consider multi-input, multi-output systems that can be expressed by a Finite Impulse Response (FIR) model. The parameters of the FIR model corresponding to each output are unknown but assumed sparse. We estimate these parameters using the Recursive Least Squares algorithm. The estimates are then improved using set-based bounds obtained by solving the Basis Pursuit Denoising problem. Our approach is able to handle hard input constraints and probabilistic output constraints. Using tools from distributionally robust optimization, we reformulate the probabilistic output constraints as tractable convex second-order cone constraints, which enables us to pose our MPC design task as a convex optimization problem. The efficacy of the developed algorithm is highlighted with a thorough numerical example, where we demonstrate performance gain over the counterpart algorithm of Bujarbaruah et al. (2018), which does not utilize the sparsity information of the system impulse response parameters during control design.} }
Endnote
%0 Conference Paper %T Exploiting Model Sparsity in Adaptive MPC: A Compressed Sensing Viewpoint %A Monimoy Bujarbaruah %A Charlott Vallon %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-bujarbaruah20a %I PMLR %P 137--146 %U https://proceedings.mlr.press/v120/bujarbaruah20a.html %V 120 %X This paper proposes an Adaptive Stochastic Model Predictive Control (MPC) strategy for stable linear time-invariant systems in the presence of bounded disturbances. We consider multi-input, multi-output systems that can be expressed by a Finite Impulse Response (FIR) model. The parameters of the FIR model corresponding to each output are unknown but assumed sparse. We estimate these parameters using the Recursive Least Squares algorithm. The estimates are then improved using set-based bounds obtained by solving the Basis Pursuit Denoising problem. Our approach is able to handle hard input constraints and probabilistic output constraints. Using tools from distributionally robust optimization, we reformulate the probabilistic output constraints as tractable convex second-order cone constraints, which enables us to pose our MPC design task as a convex optimization problem. The efficacy of the developed algorithm is highlighted with a thorough numerical example, where we demonstrate performance gain over the counterpart algorithm of Bujarbaruah et al. (2018), which does not utilize the sparsity information of the system impulse response parameters during control design.
APA
Bujarbaruah, M. & Vallon, C.. (2020). Exploiting Model Sparsity in Adaptive MPC: A Compressed Sensing Viewpoint. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:137-146 Available from https://proceedings.mlr.press/v120/bujarbaruah20a.html.

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