Differentially-Private Distributed Model Predictive Control of Linear Discrete-Time Systems with Global Constraints

TL;DR

This paper introduces a differentially-private distributed model predictive control method for linear systems with global constraints, ensuring privacy, convergence, and stability.

Contribution

It develops a novel privacy-preserving DMPC algorithm using noise injection that guarantees convergence, optimality, and privacy for coupled systems.

Findings

Ensures $ ext{epsilon}$-differential privacy in DMPC.

Guarantees recursive feasibility and stability.

Demonstrates effectiveness through simulations.

Abstract

Distributed model predictive control (DMPC) has attracted extensive attention as it can explicitly handle system constraints and achieve optimal control in a decentralized manner. However, the deployment of DMPC strategies generally requires the sharing of sensitive data among subsystems, which may violate the privacy of participating systems. In this paper, we propose a differentially-private DMPC algorithm for linear discrete-time systems subject to coupled global constraints. Specifically, we first show that a conventional distributed dual gradient algorithm can be used to address the considered DMPC problem but cannot provide strong privacy preservation. Then, to protect privacy against the eavesdropper, we incorporate a differential-privacy noise injection mechanism into the DMPC framework and prove that the resulting distributed optimization algorithm can ensure both provable convergence to a global optimal solution and rigorous $\epsilon$-differential privacy. In addition, an implementation strategy of the DMPC is designed such that the recursive feasibility and stability of the closed-loop system are guaranteed. Simulation results are provided to demonstrate the effectiveness of the developed approach.