Learning solutions to hybrid control problems using Benders cuts

Sandeep Menta, Joseph Warrington, John Lygeros, Manfred Morari
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:118-126, 2020.

Abstract

Hybrid control problems are complicated by the need to make a suitable sequence of discrete decisions related to future modes of operation of the system. Model predictive control (MPC) encodes a finite-horizon truncation of such problems as a mixed-integer program, and then imposes a cost and/or constraints on the terminal state intended to reflect all post-horizon behaviour. However, these are often ad hoc choices tuned by hand after empirically observing performance. We present a learning method that sidesteps this problem, in which the so-called N-step Q-function of the problem is approximated from below, using Benders’ decomposition. The function takes a state and a sequence of N control decisions as arguments, and therefore extends the traditional notion of a Q-function from reinforcement learning. After learning it from a training process exploring the state-input space, we use it in place of the usual MPC objective. We take an example hybrid control task and show that it can be completed successfully with a shorter planning horizon than conventional hybrid MPC thanks to our proposed method. Furthermore, we report that Q-functions trained with long horizons can be truncated to a shorter horizon for online use, yielding simpler control laws with apparently little loss of performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-menta20a, title = {Learning solutions to hybrid control problems using Benders cuts}, author = {Menta, Sandeep and Warrington, Joseph and Lygeros, John and Morari, Manfred}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {118--126}, 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/menta20a/menta20a.pdf}, url = {https://proceedings.mlr.press/v120/menta20a.html}, abstract = {Hybrid control problems are complicated by the need to make a suitable sequence of discrete decisions related to future modes of operation of the system. Model predictive control (MPC) encodes a finite-horizon truncation of such problems as a mixed-integer program, and then imposes a cost and/or constraints on the terminal state intended to reflect all post-horizon behaviour. However, these are often ad hoc choices tuned by hand after empirically observing performance. We present a learning method that sidesteps this problem, in which the so-called N-step Q-function of the problem is approximated from below, using Benders’ decomposition. The function takes a state and a sequence of N control decisions as arguments, and therefore extends the traditional notion of a Q-function from reinforcement learning. After learning it from a training process exploring the state-input space, we use it in place of the usual MPC objective. We take an example hybrid control task and show that it can be completed successfully with a shorter planning horizon than conventional hybrid MPC thanks to our proposed method. Furthermore, we report that Q-functions trained with long horizons can be truncated to a shorter horizon for online use, yielding simpler control laws with apparently little loss of performance.} }
Endnote
%0 Conference Paper %T Learning solutions to hybrid control problems using Benders cuts %A Sandeep Menta %A Joseph Warrington %A John Lygeros %A Manfred Morari %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-menta20a %I PMLR %P 118--126 %U https://proceedings.mlr.press/v120/menta20a.html %V 120 %X Hybrid control problems are complicated by the need to make a suitable sequence of discrete decisions related to future modes of operation of the system. Model predictive control (MPC) encodes a finite-horizon truncation of such problems as a mixed-integer program, and then imposes a cost and/or constraints on the terminal state intended to reflect all post-horizon behaviour. However, these are often ad hoc choices tuned by hand after empirically observing performance. We present a learning method that sidesteps this problem, in which the so-called N-step Q-function of the problem is approximated from below, using Benders’ decomposition. The function takes a state and a sequence of N control decisions as arguments, and therefore extends the traditional notion of a Q-function from reinforcement learning. After learning it from a training process exploring the state-input space, we use it in place of the usual MPC objective. We take an example hybrid control task and show that it can be completed successfully with a shorter planning horizon than conventional hybrid MPC thanks to our proposed method. Furthermore, we report that Q-functions trained with long horizons can be truncated to a shorter horizon for online use, yielding simpler control laws with apparently little loss of performance.
APA
Menta, S., Warrington, J., Lygeros, J. & Morari, M.. (2020). Learning solutions to hybrid control problems using Benders cuts. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:118-126 Available from https://proceedings.mlr.press/v120/menta20a.html.

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