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arXiv · 2109.02347

Discrete-Time Linear-Quadratic Regulation via Optimal Transport

Mathias Hudoba de Badyn·Erik Miehling·Dylan Janak·Behçet Açıkmeşe·Mehran Mesbahi·Tamer Başar·John Lygeros·Roy S. Smith
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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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Mathias Hudoba de Badyn, Erik Miehling, Dylan Janak, Behçet Açıkmeşe, Mehran Mesbahi, Tamer Başar, John Lygeros, Roy S. Smith. 2021-09-06. Discrete-Time Linear-Quadratic Regulation via Optimal Transport. https://arxiv.org/abs/2109.02347

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