Resilient Multi-Dimensional Consensus and Distributed Optimization against Agent-Based and Denial-of-Service Attacks

In this paper, we consider the resilient multi-dimensional consensus and distributed optimization problems of multi-agent systems (MASs) in the presence of both agent-based and denial-of-service (DoS) attacks. The considered agent-based attacks can cover malicious, Byzantine, and stubborn agents. The links between agents in the network can be blocked by DoS attacks, which may lead the digraph to be time-varying and even disconnected. The objective is to ensure that the remaining benign agents achieve consensus. To this end, an "auxiliary point"-based resilient control algorithm is proposed for MASs. Under the proposed algorithm, each healthy agent constructs a "safe kernel" utilizing the states of its in-neighbors and updates its state toward a specific point within this kernel at each iteration. If an agent cannot receive its neighbors' states owing to DoS attacks, it will use the states received immediately before the DoS period. Moreover, a resilient multi-dimensional distributed optimization (RMDO) algorithm is also proposed. Theoretical proofs and numerical examples are presented to demonstrate the effectiveness of the proposed algorithms.