Event-Triggered Feedback Control for Nonlinear Parabolic Distributed Parameter Systems With Time-Varying Delays
Yaqiang Liu, Weili Zhang, Jun‐Wei Wang, Yanhong Liu, Jinzhu Peng
Abstract
This paper presents an innovative event-triggered control approach for a class of nonlinear parabolic distributed parameter systems with time-varying delays. The novel event triggering mechanism enables control or measurement signals to be updated only when a predefined trigger condition exceeds a specified threshold. Multiple actuators and sensors, strategically distributed at specific points or partial regions of the spatial domain, are employed to perform pointwise/piecewise control and measurement. Two variations of event-triggered feedback (ETF) controllers are designed to address the collocated and non-collocated observation cases based on the distributions of actuators and sensors in space, respectively. The well-posedness of the open-loop and closed-loop systems is analyzed via the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{0}$ </tex-math></inline-formula>-semigroup theory, respectively. Furthermore, the non-existence of zeno behavior is guaranteed by demonstrating that the inter-event time intervals are nontrivial. Finally, the proposed method is applied to address the temperature control problem in the catalytic reaction process. Numerical simulation results validate the effectiveness of the proposed ETF control method in practical applications. Note to Practitioners—This work is motivated by the temperature control challenges in catalytic reaction process, with an extended application to the production of hot-rolled steel strips. This paper proposes an innovative event-triggered control method to reduce the demands on communication and computational resources. Extensive comparative experimental results have thoroughly validated the effectiveness of the proposed method in practical applications.