Distributed Optimization Algorithms for MASs With Network Attacks: From Continuous-Time to Event-Triggered Communication

In this paper, the distributed optimization problem for multi-agent systems under the existence of cyber attacks is researched. Each agent has a private local cost function which is assumed to be continuously differentiable and strongly convex with the Lipschitz continuous gradient. The global objective function is the sum of these local cost functions, and the communication topologies among agents are balanced and directed. Unlike most multi-agent systems in the existing literature, the cyber attacks in networks, which may result in the failure of information transmission, are considered. Two novel distributed optimization algorithms with the continuous-time communication are studied for such an optimization problem. In addition, in order to reduce computation and communication consumption efficiently, we further enhance these algorithms with an event-triggered communication mechanism. Under some assumptions and restrictions on attacks, sufficient yet efficient conditions for the convergence of the proposed algorithms are derived. Furthermore, the Zeno-behavior is shown to be excluded for the event-triggered distributed optimization algorithms. Finally, some numerical simulation examples are provided to illustrate and validate the efficiency of the proposed optimization algorithms.