Event-Based Multiagent Consensus Control: Zeno-Free Triggering via $\mathcal{L}^p$ Signals

In this paper, we develop some new event-triggered algorithms for achieving distributed consensus for a multiagent system that guarantees fully Zeno-free triggerings for all the agents. In the proposed framework, each agent updates its control input only at its own triggering instants by using local measurements (i.e., relative states) with respect to neighboring agents, and such local measurements can be done in a local coordinate frame. For all agents, a positive L
^p
signal function is embedded in the event detector functions, which aims to avoid the possible comparison of an event error term to a zero threshold that may happen in a zero-crossing scenario. We further propose a Zeno-free self-triggered algorithm to achieve multiagent consensus, which enables discrete-time measurements and thus avoids continuous measurements between the neighboring agents. We also show that the proposed event-based consensus algorithms guarantee less frequent triggered events in a bounded time interval compared to the conventional algorithm without L
^p
signals. Simulations and comparisons are provided to validate the performance and effectiveness of the proposed event-based consensus schemes.