Adaptive PI Parameter Identification and Synchronous Control of Heat Equations Modeled Multi-Agent Systems

This paper addresses the temperature synchronization control challenge in a thermal pipeline system, which is modeled using a networked heat equation. Leveraging adaptive and PID control methodologies, an adaptive PI synchronization consensus protocol is formulated. This protocol generates a target tracking signal for the temperature output of each pipeline, thereby steering the temperature output of the pipelines accordingly. In response to the output tracking error, a synchronization controller and an infinite-dimensional observer are designed to counteract external disturbances and attain output synchronization of the system temperature. Simulation outcomes substantiate the efficacy of the proposed controller.