A Distributionally Robust Optimal Control Approach for Differentially Private Dynamical Systems

TL;DR

This paper introduces a distributionally robust optimal control framework for differentially private dynamical systems, allowing secure outsourcing of control while accounting for uncertainty in noise distribution, and provides a tractable solution via convex relaxation.

Contribution

It proposes a novel distributionally robust control method that handles ambiguity in noise distribution for privacy-preserving systems, with a tractable convex reformulation.

Findings

Provides a convex relaxation of the ambiguity set.

Derives a closed-form solution for the robust control problem.

Enables secure control outsourcing with privacy guarantees.

Abstract

In this paper, we develop a distributionally robust optimal control approach for differentially private dynamical systems, enabling a plant to securely outsource control computation to an untrusted remote server. We consider a plant that ensures differential privacy of its state trajectory by injecting calibrated noise into its output measurements. Unlike prior works, we assume that the server only has access to an ambiguity set consisting of admissible noise distributions, rather than the exact distribution. To account for this uncertainty, the server formulates a distributionally robust optimal control problem to minimize the worst-case expected cost over all admissible noise distributions. However, the formulated problem is computationally intractable due to the nonconvexity of the ambiguity set. To overcome this, we relax it into a convex Kullback--Leibler divergence ball, so that the reformulated problem admits a tractable closed-form solution.