Distributed dynamic event-triggered mechanisms for time-varying distributed optimization

In this paper, a distributed dynamical event-triggered control mechanism (DETCM) and a distributed intermittent DETCM for time-varying distributed optimization problems (TVDOPs) are proposed. The distributed DETCM guarantees that all state trajectories in multiagent systems converge to the optimal solution for TVDOPs without the inverse Hessian matrix and the identical Hessian matrix of time-varying cost function. This mechanism prevents the occurrence of a phenomenon that the actuator frequently executes due to an infinite number of triggers. In order to alleviate the control cost, one distributed intermittent DETCM is proposed for TVDOPs, in which the overall average of all agents information is employed. The algorithm convergence of this mechanism can be also analyzed without the identical Hessian matrix of time-varying cost function. One dynamical event-triggered condition is introduced to avoid the occurrence of the Zeno behavior. One example from the micro-grids application is given to show the usefulness of the theoretical results obtained.