Integral barrier lyapunov functions-based adaptive fuzzy event-triggered fault tolerant control for PDE-ODE cascade systems with state constraints
摘要
This paper develops an adaptive fuzzy event-triggered fault-tolerant control framework for parabolic partial differential equation (PDE)-ordinary differential equation (ODE) cascade systems subject to state constraints. Initially, both infinite and finite-dimensional backstepping methods are employed to design the control schemes. Specifically, the original PDE subsystem is transformed into a simplified representation through an infinite-dimensional backstepping transformation and its inverse, which substantially streamlines the controller synthesis process. Subsequently, for the derived PDE-ODE cascade system, integral Barrier Lyapunov functions are introduced at each step of the finite-dimensional backstepping-based control design procedure. This formulation is demonstrated to effectively enforce direct state-variable constraints through rigorous Lyapunov-based analysis. To further enhance robustness, fuzzy logic systems are integrated with the backstepping framework, enabling the derivation of an adaptive compensation mechanism capable of mitigating actuator faults. Additionally, an event-triggered mechanism is incorporated into the design to reduce data transmission. Finally, the effectiveness of the proposed control strategy is validated through a simulation example.