Event-Triggered Predefined-Time Distributed Optimization for Second-Order Multiagent Systems via Sliding Mode

In this letter, the predefined-time distributed robust optimization is studied for disturbed second-order multiagent systems under the event-triggering mechanism. To this end, a sliding mode-based hierarchical control scheme is presented. In the first part, a local reference output signal with predefined-time convergence is generated by the proposed time-varying functions (TVFs)-based event-triggered local-minimization-free zero-gradient-sum (LMFZGS) algorithm and evolves to the global cost function’s minimizer. In the second part, a TVFs-based predefined-time sliding mode tracking controller is designed to drive the agents’ outputs to track the local reference output, regardless of lumped disturbances. By this scheme, all agents’ outputs can reach the global minimizer, characterized by predefined-time convergence, with only the virtual output signal required to be shared among agents. Simulation results demonstrate the effectiveness of our scheme.