A first-order condition for discrete-time distribution steering

2025/08/28 by Corella, Alberto Domínguez, González-Sánchez, David
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2508.21026

Abstract

We study a class of distribution-steering problems from a variational point of view. Under some differentiability assumptions, we derive necessary conditions for optimal Markov policies in the spirit of the Lagrange multiplier approach. We also provide a heuristic gradient-based method derived from the variational principle.

Citations

• Discrete-Time Linear-Quadratic Regulation via Optimal Transport
• Covariance Control of Discrete-Time Gaussian Linear Systems Using Affine Disturbance Feedback Control Policies
• Necessary Optimality Conditions for Optimal Control Problems in Wasserstein Spaces
• The Pontryagin Maximum Principle in the Wasserstein Space
• On the relation between optimal transport and Schrödinger bridges: A stochastic control viewpoint
• Optimal steering of a linear stochastic system to a final probability distribution, Part III
• Optimal steering of a linear stochastic system to a final probability distribution, part II
• Optimal steering of a linear stochastic system to a final probability distribution

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