Event‐triggered observation‐based boundary control for multi‐agent system with non‐collocated measurement

This article tackles the problem of achieving state consistency in a multi‐agent system described by parabolic partial differential equation (PDE) through the design of a non‐collocated distributed observer with event triggering. We develop a Luenberger PDE observer utilizing an event‐triggered mechanism based on output errors to exponentially track the system's state. A feedback controller is introduced that relies on the estimated state. This approach ensures the consistency of the multi‐agent system through boundary control and achieves convergence of the observer to the true system state. Using the Lyapunov technique, we show that the state error is uniformly bounded and the observation error is exponentially stable. Additionally, we provide a rigorous proof of the presence of a minimum time interval between triggering events.