A Distributionally Robust Optimal Control Approach for Differentially Private Dynamical Systems
This work addresses privacy and security challenges in control systems for applications like cloud-based automation, though it is incremental as it builds on prior differential privacy methods.
The paper tackles the problem of securely outsourcing control computation for differentially private dynamical systems by developing a distributionally robust optimal control approach that accounts for uncertainty in noise distributions, resulting in a tractable closed-form solution.
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.