Fully distributed optimization of second-order systems with disturbances based on event-triggered control

This paper studies the distributed optimization problem of second-order multiagent systems containing external disturbances. To reject the external disturbances and lead agents' states to converge to the optimal consensus point, an adaptive event-triggered controller is proposed based on the internal model principle. With the adaptive mechanism, both the controller and the event-triggering condition do not contain the parameters related to global information, such as the maximum Lipschitz constant and the minimum strongly convex constant of local cost functions, and hence the event-triggered controller is fully distributed. By utilizing the event-triggered scheme, the consumption of communication among neighbors and the computing resources are saved. Furthermore, with the Lyapunov analysis framework, the optimal consensus can be proved to achieve and Zeno behavior is excluded from the event-triggering condition. Finally, the effectiveness of the proposed protocol is verified by numerical simulations.