Event-Triggered Fuzzy Adaptive Stabilization of Parabolic PDE–ODE Systems

Artificial intelligence (AI) offers fuzzy logic system (FLS) technique as one of the popular AI agents and decision-making tools for control systems to deal with uncertain nonlinearities. This article is concerned with the event-triggered intelligent fuzzy adaptive stabilization of a class of reaction-diffusion systems based on parabolic partial differential equations-ordinary differential equations (PDE–ODEs). The studied system type is an ODE subsystem with nonlinear and unknown control coefficients for controlling PDEs. The original PDE is transformed into a new target system through the infinite-dimensional transformation method, and a state feedback controller for the transformed system is designed with the adaptive backstepping method to stabilize the system. An event-triggered strategy based on a relative threshold is designed into the backstepping framework. When the triggering condition of the system is met, the control signal of the ODE subsystem is updated. The designed control scheme ensures that all closed-loop signals are bounded; in addition, the original system states can converge to zero. Finally, the simulation example demonstrates that the event-triggered control (ETC)-based stability control technology has a good control effect.