  In networked control applications, event-triggering mechanisms (ETMs) reduce
the communication load while ensuring performance guarantees. However, the
design of ETMs is becoming increasingly complex, particularly for decentralized
multi-agent and consensus setups, where the condition used to trigger
communication might incorporate the agent's local information and the
information received from neighbors. This typically results in ad-hoc
solutions, which may only work for the consensus protocols under consideration.
In this work, we aim to safely incorporate neural networks in the ETM to
provide a general and flexible solution while ensuring guaranteed performance.
To decouple the stability analysis of the consensus protocol from the
abstraction of the neural network in the ETM, we first derive design criteria
for the consensus and ETM pair, which allow independent analysis of each
element under mild constraints. As a result, we propose NN-ETM, a novel ETM
featuring a neural network, which provides an all-purpose solution to optimize
communication in consensus problems while preserving the stability guarantees
of the consensus protocol.
