Event-Triggered Resilient Strategy for Distributed Optimization With Unreliable Agents

In this paper, we investigate the distributed optimization problem in the presence of unreliable agents who transmit unfavorable state information to their neighbors, resulting in misbehavior among cooperative agents. This gives rise to untrustworthy interactive information between agents. To overcome this challenge, we propose observer-based and sample-and-hold-based event-triggered resilient optimization strategies, complemented by threshold-based detection and isolation strategies. These strategies enhance the system's robustness against unreliable agents and enable cooperative agents to identify and disregard interaction information from unreliable neighbors. The system exhibits right-discontinuity due to intermittently changing communication networks and event-triggered time sequences. To analyze the convergence of nonsmooth systems, we integrate Filippov's differential inclusions with Lyapunov stability theory. Finally, we validate the efficacy of the proposed algorithms through comprehensive simulation results.