  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 goal 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. In addition, to reduce the communication
overhead, we propose an event-triggered communication scheme and show that the
constant regret bound and sublinear fit bound are still achieved in the case of
discrete communications with no Zeno behavior. A numerical example is provided
to verify the proposed algorithms.with no Zeno behavior. A numerical example is
provided to verify the proposed algorithms.
