Adaptive fuzzy dynamic event-triggered control for PDE-ODE cascaded systems with actuator failures

Abstract

This paper investigates the adaptive stabilization control for partial differential equation (PDE) – ordinary differential equation (ODE) cascaded systems with actuator failures. Since the systems under consideration involve unknown nonlinear functions, fuzzy logic systems are employed to approximate these functions. Additionally, an approach combining infinite and finite-dimensional backstepping methods with adaptive dynamic compensation techniques is utilized to solve the control problem for PDE-ODE cascaded systems. Specifically, an infinite-dimensional backstepping transformation and its inverse are utilized to convert the original PDE subsystem into a target system, thereby simplifying the control design process. To further optimize the controller design, a first-order filter is incorporated into the finite-dimensional backstepping method to mitigate the “explosion of complexity” issue. Moreover, a dynamic event-triggered mechanism is introduced to save communication resources. Ultimately, the proposed control algorithm guarantees that all signals remain bounded, and this is validated through a simulation example.