A new event-triggered internal model-based observer method for cooperative robust output regulation

This paper addresses the distributed cooperative robust output regulation problem of nonlinear multi-agent systems in normal form with nonidentical relative degrees. First, a new distributed event-triggered internal model-based observer is proposed to estimate the exosystem with uncertain parameters in its output. To ensure that the estimation error of the observer converges to 0 asymptotically without using continuous communication between neighboring agents, a novel reduced-order event-triggering mechanism together with an estimator for the observer is introduced to determine appropriate communication instants for each agent. It is shown that Zeno behavior is excluded by providing a strict positive minimum inter-event time. Second, distributed controllers are designed using the backstepping method to enable individual agents to track the observers. It is demonstrated that the proposed event-triggered control protocol can solve the concerned problem under fixed communication digraphs containing a spanning tree. Third, jointly connected digraphs are considered. Unlike fixed digraphs, it is found that the system matrix of the internal model-based observer needs to satisfy additional conditions, such as having small enough traces, to achieve the control objective. Finally, numerical examples are conducted to demonstrate the effectiveness of the proposed event-triggered control protocols.