Discrete-Time Linear-Quadratic Regulation via Optimal Transport
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Date
2021
Publication Type
Conference Paper
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yes
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Abstract
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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published
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Editor
Book title
2021 60th IEEE Conference on Decision and Control (CDC)
Journal / series
Volume
Pages / Article No.
3060 - 3065
Publisher
IEEE
Event
60th Conference on Decision and Control (CDC 2021)
Edition / version
Methods
Software
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Date collected
Date created
Subject
Electrical engineering; control theory; MULTI-AGENT SYSTEMS (ARTIFICIAL INTELLIGENCE); optimal transport
Organisational unit
08814 - Smith, Roy (Tit.-Prof.) (ehemalig) / Smith, Roy (Tit.-Prof.) (former)
03751 - Lygeros, John / Lygeros, John
Notes
Conference lecture held on December 15, 2021
Funding
Related publications and datasets
Is supplemented by: https://doi.org/10.3929/ethz-b-000476432