Event-triggered design for multi-agent optimal consensus of Euler-Lagrangian systems

In this paper, a distributed optimal consensus problem is investigated to achieve the optimization of the sum of local cost function for a group of agents in the Euler-Lagrangian (EL) system form. We consider that the local cost function of each agent is only known by itself and cannot be shared with others, which brings challenges in this distributed optimization problem. A novel gradient-based distributed continuous-time algorithm with the parameters of EL system is proposed, which takes the distributed event-triggered control mechanism into account. A sufficient condition is given to show that the performance of the global convergence to the optimal point can be guaranteed under the proposed method. Moreover, the Zeno behavior of triggering time can be excluded. Finally, to show the effectiveness of the presented algorithm, an example is given along with simulation results.