Resilient distributed optimization algorithm against adversarial attacks

As the cyber-Attack is becoming one of the most challenging threats faced by cyber-physical systems, investigating the effect of cyber-Attacks on distributed optimization and designing resilient algorithms are of both theoretical merits and practical values. Most existing works are established on the assumption that the maximum tolerable number of attacks, which depends on the network connectivity, is known by all normal agents. All normal agents will use the maximum number of attacks to decide whether the received information will be used for iterations. In this article, we relax this assumption and propose a novel resilient distributed optimization algorithm. The proposed algorithm exploits the trusted agents which cannot be compromised by adversarial attacks and form a connected dominating set in the original graph to constrain effects of adversarial attacks. It is shown that local variables of all normal and trusted agents converge to the same value under the proposed algorithm. Further, the final solution belongs to the convex set of minimizers of the weighted average of local cost functions of all trusted agents. The upper bound of the distance between the final solution and the optimal one has also been provided. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm.