Mean-covariance turnpikes in Wasserstein distributionally robust linear-quadratic control

Yanzhi Wu; Zhengping Ji

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arXiv · 2608.26986

Mean-covariance turnpikes in Wasserstein distributionally robust linear-quadratic control

Yanzhi Wu·Zhengping Ji

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Abstract

We study long-horizon Wasserstein-penalized minimax control for discrete-time stochastic linear systems with empirical disturbance data, in which adversarial disturbance distributions induce time-varying mean and covariance dynamics, making standard turnpike arguments not directly applicable. For possibly uncentered data, we characterize the generally nonzero mean reference through a reduced convex-concave Hamiltonian saddle problem. We prove horizon-uniform, two-sided exponential turnpike estimates for the mean state, adjoint, control, worst-case disturbance mean, and closed-loop covariance, showing that they spend the majority of time near static references when the horizon is long. We further construct a hybrid policy combining time-independent affine feedback with finite-horizon steering over a terminal layer, proving that its worst-case cost gap decays exponentially with the terminal-layer length uniformly in the horizon, which helps reducing the computation cost for long-horizon robust controls. Numerical examples illustrate the estimates and their dependence on the Wasserstein penalty.

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BibTeX RIS

Yanzhi Wu, Zhengping Ji. 2026-08-27. Mean-covariance turnpikes in Wasserstein distributionally robust linear-quadratic control. https://arxiv.org/abs/2608.26986

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