arXiv subjects

Dylan Janak

Publications and source records attributed to Dylan Janak.

2 recordsLinked to original sources

arXiv2021

Discrete-Time Linear-Quadratic Regulation via Optimal Transport

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.

math.OC↗

arXiv2019

Maximal Invariant Set Computation and Design for Markov Chains

We describe an algorithm for computing the maximal invariant set for a Markov chain with linear safety constraints on the distribution over states. We then propose a Markov chain synthesis method that guarantees finite determination of the maximal invariant set. Although this problem is bilinear in the general case, we are able to optimize the convergence rate to a desirable steady-state distribution over reversible Markov chains by solving a Semidefinite Program (SDP), which promotes efficient computation of the maximal invariant set. We then demonstrate this approach with a decentralized swarm guidance application subject to density upper bounds.

math.OC↗