Distributed Optimization Control for Heterogeneous Multiagent Systems under Directed Topologies

This paper focuses on the solutions for the distributed optimization coordination problem (DOCP) for heterogeneous multiagent systems under directed topologies. To begin with, a different convex optimization problem is proposed, which implies a weighted average of the objective function of each agent. Sufficient conditions are set to ensure the unique solution for the DOCP. Then, despite the external disruption, a distributed control mechanism is constructed to drive the state of each agent to the auxiliary state in a finite time. Furthermore, it is demonstrated that the outputs of all agents can achieve the optimal value, ensuring global convergence. Moreover, the controller design rule is expanded with event-triggered communication, and there is no Zeno behavior. Finally, to exemplify the usefulness of the theoretical conclusions, a simulation example is offered.