Due to the urgent demands of engineering practice, the stabilization problem for parabolic PDE-ODE systems has gained wide attention in the intelligent control field. However, the problem of event-triggered intelligent adaptive stabilization for parabolic PDE-ODE systems remains open. Dealing with the adaptive stabilization problem for parabolic PDEs usually exists the coupling phenomenon. The actuator dynamics is regarded as one of the indispensable factors in the boundary conditions, but the current scheme only describes the actuator dynamics considered at the boundary points in terms of linearly controllable higher order ODE systems, and rarely with nonlinear controllable higher order ODEs. In addition, traditional periodic sampling incurs the waste of network resources, hence this article attempts to provide a simple adaptive event-triggered intelligent control method for nonlinear systems with the help of the FLS technique.

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 cont...