Continuous-Time and Event-Triggered Online Optimization for Linear Multi-Agent Systems

Yang Yu, Xiuxian Li, Li Li, Lihua Xie

Abstract: This paper studies the decentralized online convex optimization problem for heterogeneous linear multi-agent systems. Agents have access to their time-varying local cost functions related to their own outputs, and there are also time-varying coupling inequality constraints among them. The target of each agent is to minimize the global cost function by selecting appropriate local actions only through communication between neighbors. We design a distributed controller based on the saddle-point method which achieves constant regret bound and sublinear fit bound. Moreover, to diminish the communication overhead, another distributed controller is developed with an event-triggered communication scheme and it is shown that the above bounds are still achieved in the case of discrete communications with no Zeno behavior. A numerical example is given to verify the proposed algorithms.