TY - GEN
T1 - Discrete-Time Linear-Quadratic Regulation via Optimal Transport
AU - De Badyn, Mathias Hudoba
AU - Miehling, Erik
AU - Janak, Dylan
AU - Acikmese, Behcet
AU - Mesbahi, Mehran
AU - Basar, Tamer
AU - Lygeros, John
AU - Smith, Roy S.
N1 - Funding Information:
This work was supported by the ETH Foundation, and the SNSF under NCCR Automation, and the Erwin Schrödinger Institute. EM and TB are funded by US ARL Cooperative Agreement W911NF-17-2-0196, and by AFOSR grant FA9550-19-1-0353. MM is funded by AFOSR grant FA9550-16-1-0022.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a linear-quadratic regulator problem where the initial and terminal states are distributed according to specified probability densities. A closed-form solution for the optimal transport map in the case of linear-time varying systems is derived, along with an algorithm for computing the optimal map. Two numerical examples pertaining to swarm deployment demonstrate the practical applicability of the model, and performance of the numerical method.
AB - In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a linear-quadratic regulator problem where the initial and terminal states are distributed according to specified probability densities. A closed-form solution for the optimal transport map in the case of linear-time varying systems is derived, along with an algorithm for computing the optimal map. Two numerical examples pertaining to swarm deployment demonstrate the practical applicability of the model, and performance of the numerical method.
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U2 - 10.1109/CDC45484.2021.9682825
DO - 10.1109/CDC45484.2021.9682825
M3 - Conference contribution
AN - SCOPUS:85126051259
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3060
EP - 3065
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th IEEE Conference on Decision and Control, CDC 2021
Y2 - 13 December 2021 through 17 December 2021
ER -