Differentially Private Distributed Mismatch Tracking Algorithm for Constraint-Coupled Resource Allocation Problems

This paper considers privacy-concerned distributed constraint-coupled resource allocation problems over an undirected network, where each agent holds a private cost function and obtains the solution via only local communication. With privacy concerns, we mask the exchanged information with independent Laplace noise against a potential attacker with potential access to all network communications. We propose a differentially private distributed mismatch tracking algorithm (diff-DMAC) to achieve cost-optimal distribution of resources while preserving privacy. Adopting constant stepsizes, the linear convergence property of diff-DMAC in mean square is established under the standard assumptions of Lipschitz gradients and strong convexity. Moreover, it is theoretically proven that the proposed algorithm is {\epsilon}-differentially private.And we also show the trade-off between convergence accuracy and privacy level. Finally, a numerical example is provided for verification.

Distributed Dual Gradient Tracking for Economic Dispatch in Power Systems with Noisy Information

Distributed algorithms can be efficiently used for solving economic dispatch problem (EDP) in power systems. To implement a distributed algorithm, a communication network is required, making the algorithm vulnerable to noise which may cause detrimental decisions or even instability. In this paper, we propose an agent-based method which enables a fully distributed solution of the EDP in power systems with noisy information exchange. Through the novel design of the gradient tracking update and introducing suppression parameters, the proposed algorithm can effectively alleviate the impact of noise and it is shown to be more robust than the existing distributed algorithms. The convergence of the algorithm is also established under standard assumptions. Moreover, a strategy are presented to accelerate our proposed algorithm. Finally, the algorithm is tested on several IEEE bus systems to demonstrate its effectiveness and scalability.